Question

vector A of magnitude 20 units lies in the direction 45 degrees S of E, while vector B, of magnitude 30 units is in the direction 60 degrees W of N. Calculate the scaler product A.B

Answer 1

$\vec{A}*\vec{B}=| \vec{A}|| \vec{B}|\cos\theta$

$\theta_1= \angle(W,S)+45^0\text{(S of E)}+60^0\text{(W of N)}=$

$= 90^0+45^0+60^0= 195^0$

$\theta_1>180^0\text{ hence this is the outer angle}$

$\theta_1= 360^0-\theta= 165^0$

$\vec{A}*\vec{B}=| \vec{A}|| \vec{B}|\cos\theta=20*30*\cos{165^0}\approx-579.6$

Answer: -579.6 scaler product