Question

The angle between a=i+j and b=i-j is

Answer 1

draw both the vectors !
costheta = [(i+j).(i-j)]/ (magnitude of i+j).(magnitude of i-j) 

i.e,costheta=0
theta = 90

Answer 2

The angle is 90 degree.

Given:

The two vectors, a = i + j and b = i - j

Solution:

To calculate the angle between them, we need to draw the vector diagram of both.

Drawing the vectors, we get the dot product of the two vector.

From the dot product rule, we get,

$\cos \theta=\frac{\overline{a} \overline{b}}{|\overline{a}| \cdot|\overline{b}|}$

Where, $\theta$ be the angle between the two vector.

$\overline{a} \overline{b}=(1 \times 1)+(1 \times(-1))=1-1=0$

$\cos \theta=\frac{0}{|\overline{a}| \cdot|\overline{b}|}$

$\therefore \cos \theta=0$

On solving, we get,

$\theta=\cos ^{-1} 0$

$\theta=90^{\circ}$

Thereby, $\theta$ is 90 degrees to be the angle between the two vectors.