Question

Please put the letter and the answer choice that goes with it so i know which answer is for that question. (example 1. 3+3=6 or 2.T)

Answer 1

Answers:

1. Choice D
2. Choice D
3. Choice C

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Explanations:

Problem 1

A = (4,4)

B = (-12,8)

Vector u starts at A and ends at B. The arrow points to B.

Subtract x coordinates: xB - xA = -12-4 = -16

Subtract y coordinates: yB - yA = 8-4 = 4

The vector is u = <-16, 4> which is in quadrant Q2.

Use the pythagorean theorem to find the length of the vector.

a^2 + b^2 = c^2

c = sqrt( a^2 + b^2 )

||u|| = sqrt( (-16)^2 + 4^2 )

||u|| = 16.492

Now compute the angle

theta = arctan(b/a)

theta = arctan(4/(-16))

theta = -14.036

Add on 180 degrees so the angle lands in Q2.

-14.036+180 = 165.964

The angle is roughly theta = 165.964 degrees

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Problem 2

A = start point = (4, 3)

B = end point = (-4, -1)

Subtract x coordinates: xB - xA = -4 - 4 = -8

Subtract y coordinates: yB - yA = -1-3 = -4

v = <a, b> = <-8, -4> which is in Q3

Use the pythagorean theorem to find the length of the vector.

a^2 + b^2 = c^2

c = sqrt( a^2 + b^2 )

||v|| = sqrt( (-8)^2 + (-4)^2 )

||v|| = 8.944

And,

theta = arctan(b/a)

theta = arctan(-4/(-8))

theta = 26.565

We need to add on 180 so we move from Q1 to Q3

26.565+180 = 206.565

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Problem 3

The notation <-3, 4> means "move 3 units left, 4 units up".

Only vector r fits the description as we move from the initial point (5,3) to the terminal point (2,7)