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Common Core: High School - Number and Quantity : Compute Magnitude and Direction of a Scalar Multiple: CCSS.Math.Content.HSN-VM.B.5b

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Example Questions

Example Question #191 : High School: Number And Quantity

Calculate $\left \| -10v\right \|$ $\displaystyle \left \| -10v\right \|$ , where v=<-6,7> $\displaystyle v=< -6,7>$ . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| -10\:v\right \|=-\sqrt{85}$ $\displaystyle \left \| -10\:v\right \|=-\sqrt{85}$ , Direction is away from $\displaystyle v$ .

$\left \| -10\:v\right \|=-10\sqrt{85}$ $\displaystyle \left \| -10\:v\right \|=-10\sqrt{85}$ , Direction is away from $\displaystyle v$ .

$\left \| -10\:v\right \|=10\sqrt{85}$ $\displaystyle \left \| -10\:v\right \|=10\sqrt{85}$ , Direction is the same as $\displaystyle v$ .

$\left \| -10\:v\right \|=10\sqrt{85}$ $\displaystyle \left \| -10\:v\right \|=10\sqrt{85}$ , Direction is away from $\displaystyle v$ .

$\left \| -10\:v\right \|=\sqrt{85}$ $\displaystyle \left \| -10\:v\right \|=\sqrt{85}$ , Direction is the same as $\displaystyle v$ .

Correct answer:

$\left \| -10\:v\right \|=10\sqrt{85}$ $\displaystyle \left \| -10\:v\right \|=10\sqrt{85}$ , Direction is away from $\displaystyle v$ .

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.

$=10\cdot\sqrt{(-6)^2+7^2}=10\cdot\sqrt{36+49}=10\sqrt{85}$ $\displaystyle =10\cdot\sqrt{(-6)^2+7^2}=10\cdot\sqrt{36+49}=10\sqrt{85}$

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

See below for a picture.

Screen shot 2016 03 07 at 12.02.14 pm

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Example Question #192 : High School: Number And Quantity

Calculate $\left \| 7v\right \|$ $\displaystyle \left \| 7v\right \|$ , where v=<8,6> $\displaystyle v=< 8,6>$ . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 7\:v\right \|=70$ $\displaystyle \left \| 7\:v\right \|=70$ , Direction is away from $\displaystyle v$ .

$\left \| 7\:v\right \|=7$ $\displaystyle \left \| 7\:v\right \|=7$ , Direction is the same as $\displaystyle v$ .

$\left \| 7\:v\right \|=-7$ $\displaystyle \left \| 7\:v\right \|=-7$ , Direction is away from $\displaystyle v$ .

$\left \| 7\:v\right \|=-70$ $\displaystyle \left \| 7\:v\right \|=-70$ , Direction is away from $\displaystyle v$ .

$\left \| 7\:v\right \|=70$ $\displaystyle \left \| 7\:v\right \|=70$ , Direction is the same as $\displaystyle v$ .

Correct answer:

$\left \| 7\:v\right \|=70$ $\displaystyle \left \| 7\:v\right \|=70$ , Direction is the same as $\displaystyle v$ .

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.

$=7\cdot\sqrt{8^2+6^2}=7\cdot\sqrt{64+36}=7\sqrt{100}=7\cdot10=70$ $\displaystyle =7\cdot\sqrt{8^2+6^2}=7\cdot\sqrt{64+36}=7\sqrt{100}=7\cdot10=70$

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

See below for a picture.

Screen shot 2016 03 07 at 12.10.09 pm

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Common Core: High School - Number and Quantity : Compute Magnitude and Direction of a Scalar Multiple: CCSS.Math.Content.HSN-VM.B.5b

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 #191 : High School: Number And Quantity

Example Question #192 : High School: Number And Quantity

All Common Core: High School - Number and Quantity Resources

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