Question

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.

Answer 1

Answer:

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°