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Calculus 3 : Dot Product

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6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #171 : Dot Product

Find the dot product of the vectors $\left \langle 2,-4,1\right \rangle$ and $\left \langle -1,3,6\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product of two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , we apply the formula $a\cdot b=a_1b_1+a_2b_2+a_3b_3$

Using the vectors from the problem statement, we get

(2*-1)+(-4*3)+(6*1)=-8

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Example Question #172 : Dot Product

Find the dot product of the vectors $\left \langle -2,-5,-8\right \rangle$ and $\left \langle 2,-9,1\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product of two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , we apply the formula $a\cdot b=a_1b_1+a_2b_2+a_3b_3$

Using the vectors from the problem statement, we get

(2*-2)+(-5*-9)+(-8*1)=33

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Example Question #173 : Dot Product

Find the dot product of the vectors $\left \langle 2,0,-4\right \rangle$ and $\left \langle 9,4,1\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product of two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , we use the formula $a\cdot b=a_1b_1+a_2b_2+a_3b_3$

Using the vectors from the problem statement, we get

(2*9)+(0*4)+(-4*1)=14

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Example Question #174 : Dot Product

Find the dot product of the vectors $\left \langle 8,9,5\right \rangle$ and $\left \langle 0,2,-7\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product of two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , we use the formula $a\cdot b=a_1b_1+a_2b_2+a_3b_3$

Using the vectors from the problem statement, we get

(8*0)+(9*2)+(5*-7)=-17

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Example Question #171 : Dot Product

Solve:

$\left \langle x, y, z^2\right \rangle\cdot \left \langle 4, xy, 3y\right \rangle$

Possible Answers:

12x^2y^3z^2

$\left \langle 4x, xy^2,3yz^2 \right \rangle$

4x+xy^2+3yz^2

4x+x^2y^2+3yz^2

Correct answer:

4x+xy^2+3yz^2

Explanation:

The dot product of two vectors is equal to the sum of the product of the corresponding components (for example, $\left \langle a,b\right \rangle \cdot \left \langle c,d\right \rangle = ac+bd$ )

The final answer is

4x+xy^2+3yz^2

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Example Question #176 : Dot Product

Find the dot product of the vectors $\left \langle 3,-5,7\right \rangle$ and $\left \langle -6,-7,-4\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product of two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , you use the following formula

$a\cdot b=a_1b_1+a_2b_2+a_3b_3$

Using the vectors from the problem statement, we get

(3*-6)+(-5*-7)+(7*-4)=-11

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Example Question #172 : Dot Product

Find the dot product of the vectors $\left \langle -3,8,10\right \rangle$ and $\left \langle -5,-2,4\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product of two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , you use the following formula

$a\cdot b=a_1b_1+a_2b_2+a_3b_3$

Using the vectors from the problem statement, we get

(-3*-5)+(8*-2)+(10*4)=39

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Example Question #178 : Dot Product

Find the dot product of the vectors $\left \langle 8,5,1\right \rangle$ and $\left \langle 0, 10,-4\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product between two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , you use the formula:

$a\cdot b=a_1b_1+a_2b_2+a_3b_3$

Using the vectors from the problem statement, we get

(8*0)+(5*10)+(1*-4)=46

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Example Question #179 : Dot Product

Find the dot product of the vectors $\left \langle 8,5,1\right \rangle$ and $\left \langle -3, 1- 9\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product between two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , you use the formula:

$a\cdot b=a_1b_1+a_2b_2+a_3b_3$

Using the vectors from the problem statement, we get

(8*-3)+(5*1)+(1*-9)=-28

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Calculus 3 : Dot Product

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #171 : Dot Product

Example Question #172 : Dot Product

Example Question #173 : Dot Product

Example Question #174 : Dot Product

Example Question #171 : Dot Product

Example Question #176 : Dot Product

Example Question #172 : Dot Product

Example Question #178 : Dot Product

Example Question #179 : Dot Product

All Calculus 3 Resources

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