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Calculus 3 : Dot Product

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Example Questions

Example Question #151 : Dot Product

Find the dot product between the vectors $\left \langle 2,7,20\right \rangle$ and $\left \langle 5,6,1\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product between the vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the formula $a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$

Using the vectors from the problem statement, we then get

(2*5)+(7*6)+(20*1)=72

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Example Question #2464 : Calculus 3

Find the dot product between the vectors $\left \langle 1,9,6\right \rangle$ and $\left \langle -3,10,1\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product between the vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the formula $a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$

Using the vectors from the problem statement, we then get

(1*-3)+(9*10)+(6*1)=93

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Example Question #152 : Dot Product

Find the dot product between the vectors $\left \langle 3,y,1\right \rangle$ and $\left \langle 2,y^3,5\right \rangle$

Possible Answers:

11-y^4

$\left \langle 6,y^4,5\right \rangle$

12+3y^2

11+y^4

Correct answer:

11+y^4

Explanation:

To find the dot product between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the formula:
$a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$

Using the vectors from the problem statement and applying, we get

(3*2)+(y*y^3)+(1*5)=11+y^4

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Example Question #462 : Vectors And Vector Operations

Find the dot product between the vectors $\left \langle 9,9,3\right \rangle$ and $\left \langle x,2,1\right \rangle$

Possible Answers:

7x+21

9x+18

10x+21

9x+21

Correct answer:

9x+21

Explanation:

To find the dot product between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the formula:
$a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$

Using the vectors from the problem statement and applying, we get

(9*x)+(9*2)+(3*1)=9x+21

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Example Question #462 : Vectors And Vector Operations

Find the dot product of the two vectors.

u=<10,-8>

v=<3,-1>

Possible Answers:

240

Correct answer:

Explanation:

The dot product of two vectors

a=<a_1,a_2>

b=<b_1,b_2>

is defined as

$a \bullet b=a_1*b_1+a_2*b_2$

For the vectors in this problem we have

$u \bullet v=10*3+(-8)*(-1)=30+8=38$

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Example Question #153 : Dot Product

Find the dot product of the two vectors.

u=<-5,4>

v=<-3,-3>

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors

a=<a_1,a_2>

b=<b_1,b_2>

is defined as

$a \bullet b=a_1*b_1+a_2*b_2$

For the vectors in this problem we have

$u \bullet v=-5*(-3)+4*(-3)=15-12=3$

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Example Question #154 : Dot Product

Find the dot product of the two vectors.

u=<6,-7>

v=<-4,-1>

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors

a=<a_1,a_2>

b=<b_1,b_2>

is defined as

$a \bullet b=a_1*b_1+a_2*b_2$

For the vectors in this problem we have

$u \bullet v=6*(-4)+(-7)*(-1)=-24+7=-17$

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Example Question #155 : Dot Product

Find the dot product between the vectors $\left \langle 2,y,7\right \rangle$ and $\left \langle 3,4,-1\right \rangle$

Possible Answers:

4y-5

y-1

4y-1

3y-2

Correct answer:

4y-1

Explanation:

To find the dot product between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we apply the following formula:

$a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$

Using the vectors from the problem statement, we get

(2*3)+(y*4)+(7*-1)=4y-1

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Example Question #156 : Dot Product

Find the dot product between the vectors $\left \langle 5,4y,6\right \rangle$ and $\left \langle 4,4,-3\right \rangle$

Possible Answers:

16y+3

16y+5

16y+2

8y+2

Correct answer:

16y+2

Explanation:

To find the dot product between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we apply the following formula:

$a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$

Using the vectors from the problem statement, we get

(5*4)+(4y*4)+(6*-3)=16y+2

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Example Question #157 : Dot Product

Find the dot product between the vectors $\left \langle 3,5,1\right \rangle$ and $\left \langle 6,2,1\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we apply the formula

$a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$

Using the vectors from the problem statement, we get

(3*6)+(5*2)+(1*1)=29

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Calculus 3 : Dot Product

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #151 : Dot Product

Example Question #2464 : Calculus 3

Example Question #152 : Dot Product

Example Question #462 : Vectors And Vector Operations

Example Question #462 : Vectors And Vector Operations

Example Question #153 : Dot Product

Example Question #154 : Dot Product

Example Question #155 : Dot Product

Example Question #156 : Dot Product

Example Question #157 : Dot Product

All Calculus 3 Resources

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