Question

. Determine the angle of the two vectors a and b where their magnitudes are 11 units and 14 units, respectively. Their

resultant vector is 70.04.

Answer 1

Given:

$a=11,\; b=14, \; |{\bf a}+{\bf b}|=7.04$

We have

$$|{\bf a}+{\bf b}|^2=a^2+b^2-2ab\cos\theta$$

$$\cos\theta=\frac {a^2+b^2-|{\bf a}+{\bf b}|^2}{2ab}$$

$$\cos\theta=\frac {11^2+14^2-7.04^2}{2*11*14}=0.8683$$

$$\theta=29.7^{\circ}$$