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Calculus 2 : Parametric, Polar, and Vector

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

Example Questions

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 #881 : Calculus Ii

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

Possible Answers:

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

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

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

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

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 #51 : Linear Algebra

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 #52 : Linear Algebra

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

Possible Answers:

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

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

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

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

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

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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Example Question #53 : Linear Algebra

What is the vector form of i+5k ?

Possible Answers:

None of the above

$\left \langle -1,0,5\right \rangle$

$\left \langle 1,0,5\right \rangle$

$\left \langle -1,0,-5\right \rangle$

$\left \langle 1,0,-5\right \rangle$

Correct answer:

$\left \langle 1,0,5\right \rangle$

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+5k , we can derive the vector form $\left \langle 1,0,5\right \rangle$ .

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Example Question #31 : Vectors

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 -2i+5j-9k , we can derive the vector form $\left \langle -2,5,-9\right \rangle$ .

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Example Question #54 : Linear Algebra

What is the vector form of i+7k ?

Possible Answers:

$\left \langle 1,0,7\right \rangle$

$\left \langle 0,7,1\right \rangle$

$\left \langle 1,7,0\right \rangle$

$\left \langle 7,1,0\right \rangle$

$\left \langle 0,1,7\right \rangle$

Correct answer:

$\left \langle 1,0,7\right \rangle$

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 i+7k , we can derive the vector form $\left \langle 1,0,7\right \rangle$ .

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Example Question #37 : Vectors

What is the vector form of 4j-6k ?

Possible Answers:

$\left \langle -6,0,4\right \rangle$

$\left \langle 4,0,-6\right \rangle$

$\left \langle 4,-6,0\right \rangle$

$\left \langle 0,4,-6\right \rangle$

$\left \langle 0,-6,4\right \rangle$

Correct answer:

$\left \langle 0,4,-6\right \rangle$

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-6k , we can derive the vector form $\left \langle 0,4,-6\right \rangle$ .

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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 #22 : Vectors

Example Question #23 : Vectors

Example Question #881 : Calculus Ii

Example Question #21 : Vector Form

Example Question #51 : Linear Algebra

Example Question #52 : Linear Algebra

Example Question #53 : Linear Algebra

Example Question #31 : Vectors

Example Question #54 : Linear Algebra

Example Question #37 : Vectors

All Calculus 2 Resources

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