Please help with this vectors problem?

You are given two vectors A=−3.00 i+ 6.00 j and B=8.00 i+ 2.00 j. Let the counterclockwise angles be positive.

a) What angle θA, where 0≤θA<360, does A make with the +x-axis?

b) What angle θB, where 0≤θB<360, does B make with the +x-axis?

c) Vector C is the sum of A and B , so C=A +B . What angle θC, where 0≤θC<360, does C make with the +x-axis?

Answer:

The Best Answer for You are given two vectors A=−3.00 i+ 6.00 j and B=8.00 i+ 2.00 j. Let the counterclockwise angles be positive.

A = -3i + 6j

Means that the terminal side of A passes through the point (-3, 6) which is 3 units to the left of y-axis and 6 above x-axis

So if you draw a line going right and connecting the point to y-axis (distance 3) and another line going down to x-axis (distance 6)

Then you will get a right triangle.

You _should_ know your trig functions.

We want angle that the side makes with y-axis.

tan(blah) = 3/6 = 1/2 = 0.5

blah = arctan(0.5) = 26.6°

θA = blah + 90° = 116.6° = 117° to 3 significant figures

B is already is 1st quadrant so no need to add 90 or anything.

Distance 2 from x axis (opposite vertical) and 8 from y-axis (adjacent horizontal)

tan(θB) = 2.00/8.00 = 1/4 = 0.25

θB = arctan(0.25) = 14.0°

C=A +B so calculate A+B you’re not braindead so you should get this right.

−3.00 i + 6.00 j + 8.00 i + 2.00 j = 5.00i + 8.00j = C

Also in Q1

tan(θC) = 8/5

θC = 58.0°

For vectors in 3rd quadrant figure out angle from negative x-axis and then add 180°. And in 4th do it from negative y-axis and add 270°.

Best wishes!