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Calculus 2 : Calculus II

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 : Linear Algebra

Express -2i+3j in vector form.

Possible Answers:

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

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

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

None of the above

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

Correct answer:

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

Explanation:

In order to express -2i+3j in vector form, we will need to map its , , and coefficients to its -, -, and -coordinates.

Thus, its vector form is

$\left \langle -2,3,0\right \rangle$ .

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Example Question #11 : Vector Form

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

Possible Answers:

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

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

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

None of the above

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

Correct answer:

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

Explanation:

To find the vector form of 4i+4j-2k , we must map the coefficients of , , and to their corresponding , , and coordinates.

Thus, 4i+4j-2k becomes $\left \langle 4,4,-2\right \rangle$ .

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Example Question #12 : Vector Form

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

Possible Answers:

None of the above

$\left \langle 0,-9,1\right \rangle$

$\left \langle 1,0,-9\right \rangle$

$\left \langle -9,0,1\right \rangle$

$\left \langle -9,1,0\right \rangle$

Correct answer:

$\left \langle 0,-9,1\right \rangle$

Explanation:

To find the vector form of -9j+k , we must map the coefficients of , , and to their corresponding , , and coordinates.

Thus, -9j+k becomes $\left \langle 0,-9,1\right \rangle$ .

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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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Calculus 2 : Calculus II

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #32 : Linear Algebra

Example Question #11 : Vector Form

Example Question #12 : Vector Form

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

All Calculus 2 Resources

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