Question

A vector
of magnitude 5 units and another vector ū of magnitude 3 units point in directions
differing by 60°. Find out (a) the scalar product of the two vectors and (b) the vector product of the two vectors​

Answer 1

Answer:

7.5 units

13 units

Explanation:

$|v|=5\ \text{units}$

$|u|=3\ \text{units}$

$\theta$ = Angle between the vectors = $60^{\circ}$

Scalar product is given by

$u\cdot v=|u||v|\cos\theta\\ =3\cdot 5\cdot \cos60^{\circ}\\ =7.5\ \text{units}$

The scalar product of the vectors is 7.5 units.

Vector product is given by

$u\times v=|u||v|\sin\theta\\ =3\times 5\sin60^{\circ}\\ =13\ \text{units}$

The vector product of the vectors is 13 units.