Figure 3-32 (a) Given the vectors A and B shown in Fig. 3-32 below (A = 63.0 and

Question

Figure 3-32 (a) Given the vectors A and B shown in Fig. 3-32 below (A = 63.0 and ? = 55.5?), determine B - A. Magnitude:

Direction: ? (counterclockwise from the +x axis is positive)

(b) Determine A - B without using your answer in (a).

Magnitude:

Direction: ? (counterclockwise from the +x axis is positive)

(Compare your results and see if they are opposite.)

I found the magnitude. They are both 78.4, but I can not figure out the direction. Please help me and please show work and explain. THANKS!

Explanation / Answer

Vector A = 61*cos28º*i + 61*sin28º*j Vector B = -40*cos56.5º*i + 40*sin56.6º*j Vector A = 53.86*i + 28.64*j Vector B = -22.08*i + 33.36*j B - A (subtract the components) -75.94*i + 4.72*j The vector is in the 2nd quadrant Magnitude v[75.94² + 4.72²] = 76.1 Angle = 93.6º [arctan(4.72/75.94) in the 2nd quadrant] A - B is simply the negative of B - A 75.94*i - 4.72*j the vector is in the 4th quadrant Magnitude is the same = 76.1 Angle = 274º [arctan(4.72/75.94) in the 4th quadrant] I found it hard to read the length of vector B; it looks like 40.

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