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

7.5 units

13 units

Step-by-step 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* v=|u||v|\sin\theta\\ =3* 5\sin60^(\circ)\\ =13\ \text{units}`

The vector product of the vectors is 13 units.