Question

If the vector A and B are of magnitude 4 and 3 making an angle 30 and 90 with x axis repectively the scalar product will be​

Answer 1

Given : -

Magnitude of vector A = 4

Magnitude of vector B = 3

Vectors A and B make an angle of 30 and 90 with x-axis.

To Find : -

Scalar product of both vectors.

Solution : -

First of all we need to find angle between both vector.

It is given that, A makes an angle of 30 and B makes an angle of 90 with x-axis.

Therefore angle between both vectors will be 90 - 30 = 60°

Scalar product of two vectors inclined at angle θ is given by

→ A • B = AB cosθ

By substituting the given values;

$\longrightarrow\sf AB cos\theta \\\\\longrightarrow 4 \times 3 \times cos60^{\circ} \\\\\longrightarrow 12 \times \dfrac{1}2} \\\\\longrightarrow 6$