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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| -3v\right \|$ , where v=<0,2> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| -3\:v\right \|=6$ , Direction is the same as .

$\left \| -3\:v\right \|=6$ , Direction is away from .

$\left \| -3\:v\right \|=-6$ , Direction is away from .

$\left \| -3\:v\right \|=3$ , Direction is the same as .

$\left \| -3\:v\right \|=-3$ , Direction is away from .

Correct answer:

$\left \| -3\:v\right \|=6$ , Direction is away from .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=3\cdot\sqrt{0^2+2^2}=3\cdot\sqrt{0+4}=3\sqrt{4}=3\cdot2=6$

As for the direction of the vector, since c<0 , the resulting vector will be against the original vector .

See below for a picture.

Vecscale

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Example Question #2 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| 1v\right \|$ , where v=<-2,-4> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 1\:v\right \|=2\sqrt{5}$ , Direction is the same as .

$\left \| 1\:v\right \|=2$ , Direction is the same as .

$\left \| 1\:v\right \|=2\sqrt{5}$ , Direction is away from .

$\left \| 1\:v\right \|=\sqrt{5}$ , Direction is the same as .

$\left \| 1\:v\right \|=-2\sqrt{5}$ , Direction is away from .

Correct answer:

$\left \| 1\:v\right \|=2\sqrt{5}$ , Direction is the same as .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=1\cdot\sqrt{(-2)^2+(-4)^2}=1\cdot\sqrt{4+16}=1\sqrt{20}=2\sqrt{5}$

As for the direction of the vector, since c>0 , the resulting vector will be in the same direction as the original vector

. Screen shot 2016 03 07 at 10.10.02 am

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Example Question #2 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| 2v\right \|$ , where v=<1,2> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 2\:v\right \|=2$ , Direction is the same as .

$\left \| 2\:v\right \|=2\sqrt{5}$ , Direction is away from .

$\left \| 2\:v\right \|=4\sqrt{5}$ , Direction is away from .

$\left \| 2\:v\right \|=2\sqrt{5}$ , Direction is the same as

$\left \| 2\:v\right \|=\sqrt{5}$ , Direction is the same as .

Correct answer:

$\left \| 2\:v\right \|=2\sqrt{5}$ , Direction is the same as

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=2\cdot\sqrt{1^2+2^2}=2\cdot\sqrt{1+4}=2\sqrt{5}$

As for the direction of the vector, since c>0 , the resulting vector will be in the same direction as the original vector .

See below for a picture.

Screen shot 2016 03 07 at 10.16.42 am

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Example Question #83 : Vector & Matrix Quantities

Calculate $\left \| -4v\right \|$ , where v=<-3,-1> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| -4\:v\right \|=4\sqrt{10}$ , Direction is away from .

$\left \| -4\:v\right \|=4\sqrt{10}$ , Direction is the same as .

$\left \| -4\:v\right \|=-4$ , Direction is away from .

$\left \| -4\:v\right \|=-4$ , Direction is the same as .

$\left \| -4\:v\right \|=-4\sqrt{10}$ , Direction is away from .

Correct answer:

$\left \| -4\:v\right \|=4\sqrt{10}$ , Direction is away from .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=4\cdot\sqrt{(-3)^2+(-1)^2}=4\cdot\sqrt{9+1}=4\sqrt{10}$

As for the direction of the vector, since c<0 , the resulting vector will be against the original vector .

See below for a picture.

Screen shot 2016 03 07 at 10.20.27 am

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Example Question #5 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| -9v\right \|$ , where v=<1,4> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| -9\:v\right \|=9\sqrt{17}$ , Direction is the same as .

$\left \| -9\:v\right \|=9\sqrt{17}$ , Direction is away from .

$\left \| -9\:v\right \|=9$ , Direction is away from .

$\left \| -9\:v\right \|=\sqrt{17}$ , Direction is the same as .

$\left \| -9\:v\right \|=-9\sqrt{17}$ , Direction is away from .

Correct answer:

$\left \| -9\:v\right \|=9\sqrt{17}$ , Direction is away from .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=9\cdot\sqrt{1^2+4^2}=9\cdot\sqrt{1+16}=9\sqrt{17}$

As for the direction of the vector, since c<0 , the resulting vector will be against the original vector .

See below for a picture.

Screen shot 2016 03 07 at 10.32.32 am

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Example Question #84 : Vector & Matrix Quantities

Calculate $\left \| -2v\right \|$ , where v=<4,10> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| -2\:v\right \|=-4\sqrt{29}$ , Direction is away from .

$\left \| -2\:v\right \|=2\sqrt{29}$ , Direction is the same as .

$\left \| -2\:v\right \|=4\sqrt{29}$ , Direction is away from .

$\left \| -2\:v\right \|=-2\sqrt{29}$ , Direction is away from .

$\left \| -2\:v\right \|=4\sqrt{29}$ , Direction is the same as .

Correct answer:

$\left \| -2\:v\right \|=4\sqrt{29}$ , Direction is away from .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=2\cdot\sqrt{4^2+10^2}=2\cdot\sqrt{16+100}=2\sqrt{116}=4\sqrt{29}$

As for the direction of the vector, since c<0 , the resulting vector will be against the original vector .

See below for a picture.

Screen shot 2016 03 07 at 10.42.39 am

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Example Question #7 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| 10v\right \|$ , where v=<2,-1> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 10\:v\right \|=5\sqrt{5}$ , Direction is the same as .

$\left \| 10\:v\right \|=10\sqrt{5}$ , Direction is the same as .

$\left \| 5\:v\right \|=-5\sqrt{5}$ , Direction is away from .

$\left \| 10\:v\right \|=-10\sqrt{5}$ , Direction is away from .

$\left \| 10\:v\right \|=10\sqrt{5}$ , Direction is away from .

Correct answer:

$\left \| 10\:v\right \|=10\sqrt{5}$ , Direction is the same as .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=10\cdot\sqrt{2^2+(-1)^2}=10\cdot\sqrt{4+1}=10\sqrt{5}$

As for the direction of the vector, since c>0 , the resulting vector in the same direction as the original vector .

See below for a picture.

Screen shot 2016 03 07 at 10.54.13 am

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Example Question #1 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| 13v\right \|$ , where v=<0,-6> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 13\:v\right \|=13$ , Direction is the same as .

$\left \| 13\:v\right \|=78$ , Direction is away from .

$\left \| 13\:v\right \|=-13$ , Direction is away from .

$\left \| 13\:v\right \|=78$ , Direction is the same as .

$\left \| 13\:v\right \|=-78$ , Direction is away from .

Correct answer:

$\left \| 13\:v\right \|=78$ , Direction is the same as .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=13\cdot\sqrt{0^2+6^2}=13\cdot\sqrt{0+36}=13\sqrt{36}=13\cdot6=78$

As for the direction of the vector, since c>0 , the resulting vector will be in the same direction as the original vector .

See below for a picture.

Screen shot 2016 03 07 at 11.09.17 am

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Example Question #9 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| 11v\right \|$ , where v=<5,-1> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 11\:v\right \|=11\sqrt{26}$ , Direction is the same as .

$\left \| 11\:v\right \|=\sqrt{26}$ , Direction is the same as .

$\left \| 11\:v\right \|=11\sqrt{26}$ , Direction is away from .

$\left \| 11\:v\right \|=-\sqrt{26}$ , Direction is away from .

$\left \| 11\:v\right \|=-11\sqrt{26}$ , Direction is away from .

Correct answer:

$\left \| 11\:v\right \|=11\sqrt{26}$ , Direction is the same as .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=11\cdot\sqrt{5^2+(-1)^2}=11\cdot\sqrt{25+1}=11\sqrt{26}$

As for the direction of the vector, since c>0 , the resulting vector will be in the same direction as the original vector .

See below for a picture.

Screen shot 2016 03 07 at 11.45.20 am

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Example Question #10 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate $\left \| -12v\right \|$ , where v=<4,4> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| -12\:v\right \|=\sqrt{2}$ , Direction is the same as .

$\left \| -12\:v\right \|=48\sqrt{2}$ , Direction is away from .

$\left \| -12\:v\right \|=-48\sqrt{2}$ , Direction is away from .

$\left \| -12\:v\right \|=-\sqrt{2}$ , Direction is away from .

$\left \| -12\:v\right \|=48\sqrt{2}$ , Direction is the same as .

Correct answer:

$\left \| -12\:v\right \|=48\sqrt{2}$ , Direction is away from .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=12\cdot\sqrt{4^2+4^2}=12\cdot\sqrt{16+16}=12\sqrt{32}=48\sqrt{2}$

As for the direction of the vector, since c<0 , the resulting vector will be against the original vector .

See below for a picture.

Screen shot 2016 03 07 at 11.53.48 am

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All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #1 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #2 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #2 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #83 : Vector & Matrix Quantities

Example Question #5 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #84 : Vector & Matrix Quantities

Example Question #7 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #1 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #9 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Example Question #10 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

All Common Core: High School - Number and Quantity Resources

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