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GRE Subject Test: Math : Vectors & Spaces

Study concepts, example questions & explanations for GRE Subject Test: Math

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All GRE Subject Test: Math Resources

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Example Questions

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Example Question #71 : Vectors

Given points (6,0,2) and (2,0,-3) , what is the vector form of the distance between the points?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points.

That is, for any point $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , the distance is the vector $v=\left \langle b_1-a_1,b_2-a_2,b_3-a_3\right \rangle$ .

Subbing in our original points (6,0,2) and (2,0,-3) , we get:

$v=\left \langle 2-6,0-0,-3-2\right \rangle$

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

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Example Question #71 : Vectors & Spaces

Given points (-3,3,3) and (3,3,-3) , what is the vector form of the distance between the points?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points.

Subbing in our original points (-3,3,3) and (3,3,-3) , we get:

$v=\left \langle 3-(-3),3-3,-3-3\right \rangle$

$v=\left \langle 6,0,-6\right \rangle$

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Example Question #73 : Vectors

Given points (2,-1,7) and (5,1,-1) , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle -3,2,-8\right \rangle$

$\left \langle 3,2,-8\right \rangle$

$\left \langle -3,-2,-8\right \rangle$

$\left \langle -3,2,8\right \rangle$

$\left \langle 3,2,8\right \rangle$

Correct answer:

$\left \langle 3,2,-8\right \rangle$

Explanation:

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points. That is, for any point $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , the distance is the vector $v=\left \langle b_1-a_1,b_2-a_2,b_3-a_3\right \rangle$ .

Subbing in our original points (2,-1,7) and (5,1,-1) , we get:

$v=\left \langle 5-2,1-(-1),-1-7\right \rangle$

$v=\left \langle 3,2,-8\right \rangle$

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Example Question #74 : Vectors

What is the vector form of 4i-7j+2k ?

Possible Answers:

$\left \langle 4,7,2\right \rangle$

$\left \langle -4,-7,-2\right \rangle$

$\left \langle 4,-7,2\right \rangle$

$\left \langle -4,7,-2\right \rangle$

$\left \langle 4,-7,-2\right \rangle$

Correct answer:

$\left \langle 4,-7,2\right \rangle$

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-7j+2k , we can derive the vector form $\left \langle 4,-7,2\right \rangle$ .

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Example Question #75 : Vectors

What is the vector form of ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #76 : Vectors

Given points (5,2,-2) and (1,1,6) , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle -4,-1,-8\right \rangle$

$\left \langle 4,-1,8\right \rangle$

$\left \langle 4,-1,-8\right \rangle$

$\left \langle 4,1,8\right \rangle$

$\left \langle -4,-1,8\right \rangle$

Correct answer:

$\left \langle -4,-1,8\right \rangle$

Explanation:

Subbing in our original points (5,2,-2) and (1,1,6) , we get:

$v=\left \langle 1-5,1-2,6-(-2)\right \rangle$

$v=\left \langle -4,-1,8\right \rangle$

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Example Question #77 : Vectors

Given points (-7,0,5) and (0,4,2) , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle -7,-4,-3\right \rangle$

$\left \langle 7,4,3\right \rangle$

$\left \langle 7,4,-3\right \rangle$

$\left \langle 7,-4,3\right \rangle$

$\left \langle 7,-4,-3\right \rangle$

Correct answer:

$\left \langle 7,4,-3\right \rangle$

Explanation:

Subbing in our original points (-7,0,5) and (0,4,2) , we get:

$v=\left \langle 0-(-7),4-0,2-5\right \rangle$

$v=\left \langle 7,4,-3\right \rangle$

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Example Question #78 : Vectors

Given points (1,1,-1) and (0,1,-1) , what is the vector form of the distance between the points?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Subbing in our original points (1,1,-1) and (0,1,-1) , we get:

$v=\left \langle 0-1,1-1,-1-(-1)\right \rangle$

$v=\left \langle -1,0,0\right \rangle$

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Example Question #79 : Vectors

What is the vector form of 7i+6j-k ?

Possible Answers:

$\left \langle -7,-6,-1\right \rangle$

$\left \langle 7,-6,-1\right \rangle$

$\left \langle 7,6,-1\right \rangle$

$\left \langle 7,-6,1\right \rangle$

$\left \langle 7,6,1\right \rangle$

Correct answer:

$\left \langle 7,6,-1\right \rangle$

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 7i+6j-k , we can derive the vector form $\left \langle 7,6,-1\right \rangle$ .

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Example Question #80 : Vectors

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

Possible Answers:

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

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

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

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

Correct answer:

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

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

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GRE Subject Test: Math : Vectors & Spaces

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #71 : Vectors

Example Question #71 : Vectors & Spaces

Example Question #73 : Vectors

Example Question #74 : Vectors

Example Question #75 : Vectors

Example Question #76 : Vectors

Example Question #77 : Vectors

Example Question #78 : Vectors

Example Question #79 : Vectors

Example Question #80 : Vectors

All GRE Subject Test: Math Resources

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