Question

The resultant of u and v is perpendicular to u and has a magnitude equal to half of the magnitude of v.The angle between u and v is​

Answer 1

According to the question:

(u+v).u=0       (1)

|(u+v)|=|v|2       −(2)

Now, |u+v|=u2+v2+2uvcosθ−−−−−−−−−−−−−−√     −(3)[Parallelogram Law]

And from (1), we have:

u2+uvcosθ=0       −(4)

From (2) & (3)

v2+uvcosθ−−−−−−−−−√=v2

⟹cosθ=−3v/u

Also from (4) we have - cosθ=−u/v

Therefore, cosθ=−34×−1cosθ

⟹θ=cos−1(3/4−−−√)