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Calculus 3 : Vector Subtraction

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Example Questions

Example Question #11 : Vector Subtraction

Solve:

$\left \langle xy, z\right \rangle- \left \langle 3xy, z\right \rangle$

Possible Answers:

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

$\left \langle -2xy, -2z\right \rangle$

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

-2xy

Correct answer:

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

Explanation:

The difference between two vectors is given by subtracting the corresponding components (for example, $\left \langle a, b\right \rangle - \left \langle x,y\right \rangle=\left \langle a-x, b-y\right \rangle$ )

Our final answer is

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

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Example Question #2301 : Calculus 3

Find the difference between the vectors $\left \langle 4x,7y,-4z\right \rangle$ and $\left \langle 2x,0,-z\right \rangle$

Possible Answers:

$\left \langle -x,7y,-3z\right \rangle$

$\left \langle 2x,7y,-3z\right \rangle$

$\left \langle 2x,7y,-5z\right \rangle$

$\left \langle 2x,y,-3z\right \rangle$

Correct answer:

$\left \langle 2x,7y,-3z\right \rangle$

Explanation:

To find the difference between the vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a-b=\left \langle x_1-x_2,y_1-y_2,z_1-z_2\right \rangle$

Using the vectors from the problem statement, we get

$\left \langle 4x-2x,7y-0,-4z+z\right \rangle=\left \langle2x,7y,-3z\right \rangle$

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Example Question #13 : Vector Subtraction

Find the difference between the vectors $\left \langle -10,-20,30\right \rangle$ and $\left \langle 27,15,60\right \rangle$

Possible Answers:

$\left \langle -37,-35,-30\right \rangle$

$\left \langle -37,-20,-30\right \rangle$

$\left \langle -47,-35,-30\right \rangle$

$\left \langle -37,-32,-20\right \rangle$

Correct answer:

$\left \langle -37,-35,-30\right \rangle$

Explanation:

To find the difference between the vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a-b=\left \langle x_1-x_2,y_1-y_2,z_1-z_2\right \rangle$

Using the vectors from the problem statement, we get

$\left \langle-10-27,-20-15,30-60\right \rangle=\left \langle-37,-35,-30\right \rangle$

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Example Question #12 : Vector Subtraction

Find the difference between the vectors $\left \langle 4,0,8\right \rangle$ and $\left \langle 5,-6,2\right \rangle$

Possible Answers:

$\left \langle -1,5,6\right \rangle$

$\left \langle -1,6,6\right \rangle$

$\left \langle -2,6,6\right \rangle$

$\left \langle -1,-6,6\right \rangle$

Correct answer:

$\left \langle -1,6,6\right \rangle$

Explanation:

To find the difference between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we apply the following formula:

$a-b=\left \langle x_1-x_2,y_1-y_2,z_1-z_2\right \rangle$

Using the vectors from the problem statement, we get

$\left \langle 4-5,0+6,8-2\right \rangle=\left \langle -1,6,6\right \rangle$

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Example Question #15 : Vector Subtraction

Find the difference between the vectors $\left \langle 0,-5,4\right \rangle$ and $\left \langle 2,-4,3\right \rangle$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

To find the difference between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we apply the following formula:

$a-b=\left \langle x_1-x_2,y_1-y_2,z_1-z_2\right \rangle$

Using the vectors from the problem statement, we get

$\left \langle 0-2,-5+4,4-3\right \rangle=\left \langle -2,-1,1\right \rangle$

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Example Question #301 : Vectors And Vector Operations

Find the difference between the vectors $\left \langle 3x,8y,4z\right \rangle$ and $\left \langle -2x,y,2z\right \rangle$

Possible Answers:

$\left \langle 5x,7y,2z\right \rangle$

$\left \langle 5x,7y,z\right \rangle$

$\left \langle 5x,9y,2z\right \rangle$

$\left \langle 7x,7y,2z\right \rangle$

Correct answer:

$\left \langle 5x,7y,2z\right \rangle$

Explanation:

To find the difference between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a-b=\left \langle (x_1-x_2),(y_1-y_2),(z_1-z_2) \right \rangle$

Applying to the vectors from the problem statement, we get

$\left \langle (3x+2x),(8y-y),(4z-2z) \right \rangle=\left \langle 5x,7y,2z\right \rangle$

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Example Question #16 : Vector Subtraction

Find the difference between the vectors $\left \langle 5,8,9\right \rangle$ and $\left \langle 3,9,0\right \rangle$

Possible Answers:

$\left \langle 3,-1,9\right \rangle$

$\left \langle 2,-1,9\right \rangle$

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

$\left \langle 2,1,9\right \rangle$

Correct answer:

$\left \langle 2,-1,9\right \rangle$

Explanation:

To find the difference between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a-b=\left \langle (x_1-x_2),(y_1-y_2),(z_1-z_2) \right \rangle$

Applying to the vectors from the problem statement, we get

$\left \langle (5-3),(8-9),(9-0) \right \rangle=\left \langle 2,-1,9\right \rangle$

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Example Question #13 : Vector Subtraction

Find the difference between the vectors $\left \langle \sin(x),2y^2,z^3\right \rangle$ and $\left \langle 2\sin(x),5y^2,-2z^3\right \rangle$

Possible Answers:

$\left \langle -\sin(x),-3y^2,3z^3\right \rangle$

$\left \langle -\sin(x),-3y^2,4z^3\right \rangle$

$\left \langle -\sin(x),3y^2,3z^3\right \rangle$

$\left \langle -\sin(x),-3y,3z^3\right \rangle$

Correct answer:

$\left \langle -\sin(x),-3y^2,3z^3\right \rangle$

Explanation:

To find the difference of two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ we use the formula:

$a+b=\left \langle a_1-b_1,a_2-b_2,a_3-b_3\right \rangle$

Using the vectors from the problem statement, we get

$\left \langle \sin(x)-2\sin(x),2y^2-5y^2,z^3+2z^3\right \rangle=\left \langle -\sin(x),-3y^2,3z^3\right \rangle$

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Example Question #14 : Vector Subtraction

Find the difference between the vectors $\left \langle -9,0,5\right \rangle$ and $\left \langle 2,2,2\right \rangle$

Possible Answers:

$\left \langle -11,-2,3\right \rangle$

$\left \langle -11,-2,4\right \rangle$

$\left \langle -10,-2,3\right \rangle$

$\left \langle -11,2,3\right \rangle$

Correct answer:

$\left \langle -11,-2,3\right \rangle$

Explanation:

To find the difference of two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ we use the formula:

$a+b=\left \langle a_1-b_1,a_2-b_2,a_3-b_3\right \rangle$

Using the vectors from the problem statement, we get

$\left \langle -9-2,0-2,5-2\right \rangle=\left \langle -11,-2,3\right \rangle$

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Example Question #18 : Vector Subtraction

Find the difference between the vectors $\left \langle 3,4,7\right \rangle$ and $\left \langle 3,-3,2\right \rangle$

Possible Answers:

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

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

$\left \langle 0,7,5\right \rangle$

$\left \langle 0,7,4\right \rangle$

Correct answer:

$\left \langle 0,7,5\right \rangle$

Explanation:

To find the difference of two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , we use the formula:

$a+b=\left \langle a_1-b_1,a_2-b_2,a_3-b_3\right \rangle$

Using the vectors from the problem statement, we get

$\left \langle 3-3,4+3,7-2\right \rangle=\left \langle 0,7,5\right \rangle$

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Calculus 3 : Vector Subtraction

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #11 : Vector Subtraction

Example Question #2301 : Calculus 3

Example Question #13 : Vector Subtraction

Example Question #12 : Vector Subtraction

Example Question #15 : Vector Subtraction

Example Question #301 : Vectors And Vector Operations

Example Question #16 : Vector Subtraction

Example Question #13 : Vector Subtraction

Example Question #14 : Vector Subtraction

Example Question #18 : Vector Subtraction

All Calculus 3 Resources

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