Question

Find the resultant of vector a and b magnitude of a is 10 unit and b is 15 unit and angle btwn tem is 60 degree also find resultant angle

Answer 1

Given:

Vector $\vec{A}$ = 10

vector  $\vec{B}$ = 15

Angle ∅ = 60°

Resultant R is given by expression ,

$\bold{\mathff{R=\sqrt{A^2+B^2+2AB\: cos\theta}}}$

» R =√100 + 225 +2(100) (225) Cos60°

» R = √22500

or, $\vec{R}$ = 150

Angle =  $\bold{\mathff{tany=\dfrac{B\:sin\theta}{A+Bcos\:\theta}}}$

» tany = 15sin 60 / 10+15 cos60

» tany = 12.99/17.5

or, tany = 0.7423

or, y = 36.58°

$\bold{\mathff{ Resultant\:is\:150\: and\:angle\:is\:36.58^{\circ}}}$