In the figure below are three vectors. Vector A has a length of 38.0, B\'s length is 64.0, and C is 23.0. Find the following:
1. A(dot)B = ?
2. B(dot)(A+C) = ?
3. At what angles above and below the horizontal line could vector A be at so that A·B = 0?
a. 90 degrees above, 90 degrees below
b. 90 degrees above, 70 degrees below
c. 110 degrees above, 70 degrees below
d. 20 degrees above, 160 degrees below
Thanks in advance
1. angle between A and B (x)= 70 - 20 = 50
A.B = |A| |B| cos(x) = 38 x 64 x cos50 = 38 x 64 x 0.965 = 2346.88
2. B.(A+ C) = B.A + B.C
Now, A.B = B.A = 2346.88
Angle between B and C (y) = 20 + 70 = 90
B.C = |B| |C| cos(y) = 64 x 23 x cos90 = 64 x 23 x 0 = 0
so, B.(A+ C) = B.A + B.C = 2346.88 + 0 = 2346.88
3. for A.B equal to 0, angle between them must be 90.
option c) is correct.
If 110 degree above horizontal line, then angle between A and B = 110 - 20 = 90
If 70 degree below horizontal line, then angle between A and B = 70 + 20 = 90
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