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Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

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9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #14 : Vector Form

What is the vector form of -8i+2j-7k ?

Possible Answers:

$\left \langle 7, -2, 8\right \rangle$

$\left \langle 2, -8,-7\right \rangle$

$\left \langle -7, 2, -8\right \rangle$

$\left \langle -8,2,-7\right \rangle$

$\left \langle -8,-7, 2\right \rangle$

Correct answer:

$\left \langle -8,2,-7\right \rangle$

Explanation:

Given -8i+2j-7k , we need to map the , , and coefficients back to their corresponding , , and -coordinates.

Thus the vector form of -8i+2j-7k is $\left \langle -8,2,-7\right \rangle$ .

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Example Question #15 : Vector

What is the vector form of -i+3k ?

Possible Answers:

$\left \langle 3,-1,0\right \rangle$

None of the above

$\left \langle 0,-1,3\right \rangle$

$\left \langle -1,3,0\right \rangle$

$\left \langle -1,0,3\right \rangle$

Correct answer:

$\left \langle -1,0,3\right \rangle$

Explanation:

Given -i+3k , we need to map the , , and coefficients back to their corresponding , , and -coordinates.

Thus the vector form of -i+3k is $\left \langle -1,0,3\right \rangle$ .

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Example Question #362 : Parametric, Polar, And Vector

What is the vector form of 7i-4j+k ?

Possible Answers:

$\left \langle-4,1,7\right \rangle$

$\left \langle7,-4,1\right \rangle$

$\left \langle 7,-4,1\right \rangle$

$\left \langle1,-4,7\right \rangle$

$\left \langle 1,7,-4\right \rangle$

Correct answer:

$\left \langle 7,-4,1\right \rangle$

Explanation:

Given 7i-4j+k , we need to map the , , and coefficients back to their corresponding , , and -coordinates.

Thus the vector form of 7i-4j+k is

$\left \langle 7,-4,1\right \rangle$ .

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Example Question #363 : Parametric, Polar, And Vector

What is the vector form of 5i-2j+9k ?

Possible Answers:

$\left \langle 5,9,-2\right \rangle$

None of the above

$\left \langle 9,-2,5\right \rangle$

$\left \langle -2,5,9\right \rangle$

$\left \langle 5,-2,9\right \rangle$

Correct answer:

$\left \langle 5,-2,9\right \rangle$

Explanation:

Given 5i-2j+9k , we need to map the , , and coefficients back to their corresponding , , and -coordinates.

Thus the vector form of 5i-2j+9k is

$\left \langle 5,-2,9\right \rangle$ .

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Example Question #16 : Vector

What is the vector form of 2i-k ?

Possible Answers:

None of the above

$\left \langle 0,-1,2\right \rangle$

$\left \langle 2,0,-1\right \rangle$

$\left \langle -1,2, 0\right \rangle$

$\left \langle 2,-1, 0\right \rangle$

Correct answer:

$\left \langle 2,0,-1\right \rangle$

Explanation:

Given 2i-k , we need to map the , , and coefficients back to their corresponding , , and -coordinates.

Thus the vector form of 2i-k is

$\left \langle 2,0,-1\right \rangle$ .

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Example Question #21 : Vectors

What is the dot product of $a=\left \langle 7,-7,0\right \rangle$ 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 $a=\left \langle 7,-7,0\right \rangle$ and $b=\left \langle 2, -1,8\right \rangle$ , then:

$\left \langle 7,-7,0\right \rangle\times \left \langle 2, -1,8\right \rangle$

$=(7\times 2)+(-7\times -1)+(0\times 2)$

=14+7+0

=21

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Example Question #22 : Vectors

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 #25 : Vectors

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 #403 : Gre Subject Test: Math

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 #21 : Vectors

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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Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #14 : Vector Form

Example Question #15 : Vector

Example Question #362 : Parametric, Polar, And Vector

Example Question #363 : Parametric, Polar, And Vector

Example Question #16 : Vector

Example Question #21 : Vectors

Example Question #22 : Vectors

Example Question #25 : Vectors

Example Question #403 : Gre Subject Test: Math

Example Question #21 : Vectors

All Calculus 2 Resources

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