Question

If |Ā + B| = |Ā | = |B | then angle between A and B will be
(1) 90
(2) 120°
(4) 60°
(3) 0​

Answer 1

Answer:

(1)θ = 90 °

Explanation:

Let the angle between two vectors  

A  and  B  be  θ

So  

| A  +  B | ² =  | A | ² + IBI²+2IAI IBI cos θ  

Again

| A − B | ² =  | A | ² + IBI²+2IAI IBI cos θ  (180- θ)

By the given condition

| A + B | = | A − B |

So  cos  θ  

= cos ( 180 − θ )

⇒ θ = 180 − θ

⇒ θ = 90 °

Answer 2

Answer:

• $\theta = 90^{o}$

Explanation:

Let $\theta$ be the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$

$|\overrightarrow{a} + \overrightarrow{b}| = \sqrt{a^2 + b^2 + 2ab \:cos\theta} \:\:and\:\:|\overrightarrow{a} - \overrightarrow{b}| = \sqrt{a^2 + b^2 - 2ab \:cos\theta}\:\:\:\\\\(Squaring \:on \:both\:sides)$

$\implies\:\:a^2 + b^2 + 2ab \:cos\theta = a^2 + b^2 - 2ab \:cos\theta$

$\implies\:\:4ab\:cos\theta=0$

$\implies\:\:cos\theta = 0$

$\implies\:\:\theta = 90^{o}$