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?

by

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

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!

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.