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!
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.
SHOW ANSWER