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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 #32 : Vectors

What is the vector form of 4i+8j-9k ?

Possible Answers:

$\left \langle -4,-8,-9\right \rangle$

$\left \langle 4,8,9\right \rangle$

$\left \langle 4,-8,-9\right \rangle$

$\left \langle 4,-8,9\right \rangle$

$\left \langle 4,8,-9\right \rangle$

Correct answer:

$\left \langle 4,8,-9\right \rangle$

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 4i+8j-9k , we can derive the vector form $\left \langle 4,8,-9\right \rangle$ .

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Example Question #35 : Vector Form

What is the vector form of 2i+k ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 2i+k , we can derive the vector form $\left \langle 2,0,1\right \rangle$ .

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Example Question #381 : Parametric, Polar, And Vector

What is the vector form of -4j-5k ?

Possible Answers:

$\left \langle 0,4,5\right \rangle$

$\left \langle -4,0,-5\right \rangle$

$\left \langle 0,4,-5\right \rangle$

$\left \langle -4,0,5\right \rangle$

$\left \langle 0,-4,-5\right \rangle$

Correct answer:

$\left \langle 0,-4,-5\right \rangle$

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 -4j-5k , we can derive the vector form $\left \langle 0,-4,-5\right \rangle$ .

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Example Question #36 : Vector Form

What is the vector form of i+2j+3k ?

Possible Answers:

$\left \langle -1,-2,3\right \rangle$

$\left \langle 1,2,3\right \rangle$

$\left \langle 1,-2,3\right \rangle$

$\left \langle -1,2,3\right \rangle$

$\left \langle -1,-2,-3\right \rangle$

Correct answer:

$\left \langle 1,2,3\right \rangle$

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+2j+3k , we can derive the vector form $\left \langle 1,2,3\right \rangle$ .

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Example Question #41 : Vectors

What is the vector form of 7i-7k ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 7i-7k , we can derive the vector form $\left \langle 7,0,-7\right \rangle$ .

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Example Question #37 : Vector

What is the vector form of 3j+5k ?

Possible Answers:

$\left \langle 3,0,5\right \rangle$

$\left \langle 0,-3,5\right \rangle$

$\left \langle 0,3,-5\right \rangle$

$\left \langle 0,3,5\right \rangle$

$\left \langle 0,-3,-5\right \rangle$

Correct answer:

$\left \langle 0,3,5\right \rangle$

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 3j+5k , we can derive the vector form $\left \langle 0,3,5\right \rangle$ .

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Example Question #44 : Vectors

What is the vector form of -7i+2j-5k ?

Possible Answers:

$\left \langle 7,-2,-5\right \rangle$

$\left \langle 7,-2,5\right \rangle$

$\left \langle -7,-2,-5\right \rangle$

$\left \langle -7,2,-5\right \rangle$

$\left \langle 7,2,5\right \rangle$

Correct answer:

$\left \langle -7,2,-5\right \rangle$

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 -7i+2j-5k , we can derive the vector form $a=\left \langle -7,2,-5\right \rangle$ .

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Example Question #41 : Vector Form

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

Possible Answers:

$\left \langle 0,1,4\right \rangle$

$\left \langle 1,0,-4\right \rangle$

$\left \langle 0,-1,4\right \rangle$

$\left \langle 0,-1,-4\right \rangle$

$\left \langle 0,1,-4\right \rangle$

Correct answer:

$\left \langle 0,-1,4\right \rangle$

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 -j+4k , we can derive the vector form $a=\left \langle 0,-1,4\right \rangle$ .

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Example Question #42 : Vectors

What is the vector form of 2i+10j ?

Possible Answers:

$\left \langle 2,-10,0\right \rangle$

$\left \langle 2,10,0\right \rangle$

$\left \langle -2,10,0\right \rangle$

$\left \langle -2,-10,0\right \rangle$

$\left \langle 0,2,10\right \rangle$

Correct answer:

$\left \langle 2,10,0\right \rangle$

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 2i+10j , we can derive the vector form $a=\left \langle 2,10,0\right \rangle$ .

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Example Question #42 : Vector Form

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

Possible Answers:

$\left \langle 8,-8,-1\right \rangle$

$\left \langle -8,8,-1\right \rangle$

$\left \langle 8,8,1\right \rangle$

$\left \langle -8,-8,1\right \rangle$

$\left \langle 8,8,-1\right \rangle$

Correct answer:

$\left \langle -8,8,-1\right \rangle$

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 -8i+8j-k , we can derive the vector form $\left \langle -8,8,-1\right \rangle$ .

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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 #32 : Vectors

Example Question #35 : Vector Form

Example Question #381 : Parametric, Polar, And Vector

Example Question #36 : Vector Form

Example Question #41 : Vectors

Example Question #37 : Vector

Example Question #44 : Vectors

Example Question #41 : Vector Form

Example Question #42 : Vectors

Example Question #42 : Vector Form

All Calculus 2 Resources

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