Consider two vectors a~ and b~ and their resultant a~ +b~ . the magnitudes of the vectors a~ and b~ are, respectively, 18.2 and 5.1 and they act at 120◦ to each other. find the angle between the direction of the resultant vector a + b and the direction of the vector a.

15.76°

Explanation:

Hi!

Let C~ = A~ + B~

Then

C~ dot A~ = |C| |A| cos Ф

C~ dot A~ = (A~ + B~) dot A~ = |A|^2 + |B| |A| cos(120)

Therefore

cos Ф = (|A| + |B| cos(120)) / |C| = 15.65/|C|

and

|C|^2 =  |A|^2 + |B|^2 + 2 |B| |A| cos(120)

|C| = 16.261

cos Ф = 15.65/16.261

Ф = 15.76°

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