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Calculus 2 : Vector Form

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Example Questions

Example Question #218 : Algebra

What is the dot product of $a=\left \langle 4,1,-1\right \rangle$ and $b=\left \langle 2, -1,8\right \rangle$ ?

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given $a=\left \langle 4,1,-1\right \rangle$ and $b=\left \langle 2, -1,8\right \rangle$ , then:

$\left \langle 4,1,-1\right \rangle\times \left \langle 2, -1,8\right \rangle$

$=(4\times 2)+(1\times -1)+(-1\times 8)$

=8+(-1)+(-8)

=-1

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Example Question #219 : Algebra

What is the dot product of $a=\left \langle 3,0,-9\right \rangle$ and $b=\left \langle -9, 2,-3\right \rangle$ ?

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given $a=\left \langle 3,0,-9\right \rangle$ and $b=\left \langle -9, 2,-3\right \rangle$ , then:

$\left \langle 3,0,-9\right \rangle\times \left \langle -9, 2,-3\right \rangle$

$=(3\times -9)+(0\times 2)+(-9\times -3)$

=(-27)+0+27

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Example Question #21 : Vectors & Spaces

What is the vector form of $a=\left \langle 3,-2,7\right \rangle$ ?

Possible Answers:

3i-2j-7k

-3i-2j-7k

3i+2j-7k

3i+2j+7k

3i-2j+7k

Correct answer:

3i-2j+7k

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ , the vector form is $a_{1}i+a_{2}j+a_{3}k$ .

So for $a=\left \langle 3,-2,7\right \rangle$ , we can derive the vector form 3i-2j+7k .

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Example Question #22 : Vectors & Spaces

What is the vector form of $a=\left \langle -1,9,3\right \rangle$ ?

Possible Answers:

-i-9j+3k

-i-9j-3k

i-9j+3k

-i+9j+3k

i+9j+3k

Correct answer:

-i+9j+3k

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ , the vector form is $a_{1}i+a_{2}j+a_{3}k$ .

So for $a=\left \langle -1,9,3\right \rangle$ , we can derive the vector form -i+9j+3k .

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Example Question #22 : Vectors

What is the vector form of $a=\left \langle 0,2,5\right \rangle$ ?

Possible Answers:

2i+5j

2i+5k

2j+5k

None of the above

5i+2j

Correct answer:

2j+5k

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ , the vector form is $a_{1}i+a_{2}j+a_{3}k$ .

So for $a=\left \langle 0,2,5\right \rangle$ , we can derive the vector form 2j+5k .

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Example Question #23 : Vectors

What is the vector form of 5i-6j+7k ?

Possible Answers:

$\left \langle 5,-6,-7\right \rangle$

$\left \langle 5,6,-7\right \rangle$

$\left \langle 5,-6,7\right \rangle$

$\left \langle -5,-6,-7\right \rangle$

$\left \langle 5,6,7\right \rangle$

Correct answer:

$\left \langle 5,-6,7\right \rangle$

Explanation:

In order to derive the vector form, we must map the vector elements to their corresponding , , and coefficients. That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ . So for 5i-6j+7k , we can derive the vector form $\left \langle 5,-6,7\right \rangle$ .

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Example Question #24 : Vectors

What is the vector form of -2i+9j ?

Possible Answers:

$\left \langle 0,-2,9\right \rangle$

$\left \langle-2, 0, 9\right \rangle$

$\left \langle -2,9,0\right \rangle$

$\left \langle9, 0,-2\right \rangle$

None of the above

Correct answer:

$\left \langle -2,9,0\right \rangle$

Explanation:

In order to derive the vector form, we must map the vector elements to their corresponding , , and coefficients. That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ . So for -2i+9j , we can derive the vector form $\left \langle -2,9,0\right \rangle$ .

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Example Question #21 : Vector Form

What is the vector form of 7j+14k ?

Possible Answers:

$\left \langle 0,-7,14\right \rangle$

$\left \langle 0,-7,-14\right \rangle$

$\left \langle 7,0,14\right \rangle$

$\left \langle 14,7,0\right \rangle$

$\left \langle 0,7,14\right \rangle$

Correct answer:

$\left \langle 0,7,14\right \rangle$

Explanation:

In order to derive the vector form, we must map the vector elements to their corresponding , , and coefficients. That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ . So for 7j+14k , we can derive the vector form $\left \langle 0,7,14\right \rangle$ .

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Example Question #22 : Vector Form

What is the vector form of -i+9j-5k ?

Possible Answers:

$\left \langle 1,9,5\right \rangle$

$\left \langle -1,9,-5\right \rangle$

$\left \langle -1,9,5\right \rangle$

$\left \langle -1,-9,5\right \rangle$

$\left \langle -1,-9,-5\right \rangle$

Correct answer:

$\left \langle -1,9,-5\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients. That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ . So for -i+9j-5k , we can derive the vector form $\left \langle -1,9,-5\right \rangle$ .

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Example Question #23 : Vector Form

What is the vector form of -2j+4k ?

Possible Answers:

$\left \langle-2,0,4\right \rangle$

$\left \langle 0,-2,-4\right \rangle$

$\left \langle 0,-2,4\right \rangle$

$\left \langle -2,4,0\right \rangle$

$\left \langle 4,-2,0\right \rangle$

Correct answer:

$\left \langle 0,-2,4\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients. That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ . So for -2j+4k , we can derive the vector form $\left \langle 0,-2,4\right \rangle$ .

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Calculus 2 : Vector Form

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #218 : Algebra

Example Question #219 : Algebra

Example Question #21 : Vectors & Spaces

Example Question #22 : Vectors & Spaces

Example Question #22 : Vectors

Example Question #23 : Vectors

Example Question #24 : Vectors

Example Question #21 : Vector Form

Example Question #22 : Vector Form

Example Question #23 : Vector Form

All Calculus 2 Resources

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