Question

The magnitude of

A
is 3 . Vector
A
lies in the second quadrant and forms an angle of 88 degrees with the y-axis. The components, A
x
​
and A
y
​
, are closest to: A
x
​
=+0.10,A
y
​
=−3.0 A
x
​
=+3.0,A
y
​
=−0.10 A
x
​
=−3.0,A
y
​
=+0.10 A
x
​
=−0.10,A
y
​
=−3.0 A
x
​
=−0.10,A
y
​
=+3.0

Answer 1

(c) Ax = -3.0, Ay = +0.10

Explanation:

You want the coordinates of the end point of a 2nd quadrant vector that makes an angle of 88° with the y-axis.

Angle

The angle of the vector in standard position is 88° +90° = 178°, nearly coincident with the -x axis.

Coordinates

The coordinates of the endpoint are ...

3(cos(178°), sin(178°)) ≈ (-3.00, +0.10)

The components are closest to Ax = -3.0, Ay = +0.10.

__

Additional comment

The attached calculator display shows the vector being represented as a complex number. The imaginary (i) component aligns with the +y axis.

Coordinates in the 2nd quadrant are negative for x, and positive for y. That eliminates all but choices C and E. The vector described by choice E makes an angle of 88° with the -x axis. (It can help to draw yourself a picture, as shown in the second attachment.)

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