Question

Two vectors have magnitude 3 unit and 4 unit respectively what should be the angle between them if the magnitude of the resultant is (a)1unit (b) 5 unit and (c) 7 unit

Answer 1

the formula for resultant is,
$R^2=P^2+Q^2+2PQ cos(\theta)$
$cos(\theta)=\frac{R^2-P^2-Q^2}{2PQ}$
putting P=3, Q=4 and R=1 for a, 5 for b and 7 for c gets you the cosine of the angle between them. You take the inverse cosine to get your desired answer after that.