Question

if |v1+v2| vector = |v1-v2| vector then find the angle between v1 and v2 vector

Answer 1

Given:

$| \vec v_{1} + \vec v_{2} | = | \vec v_{1} - \vec v_{2} |$

This relationship between the two vectors v1 and v2 has been provided.

To find:

Angle between $\vec v_{1}$ and $\vec v_{2}$

Calculation:

Let the angle between the vectors be $\theta$

Now , we can also say that the angle between $\vec v_{1}$ and $-\vec v_{2}$ is $(180° - \theta)$

The 2nd angle will help in calculation of subtraction of coplanar vectors as provided in the question.

$\therefore \: | \vec v_{1} + \vec v_{2} | = | \vec v_{1} - \vec v_{2} |$

$= > \sqrt{ {(v_{1})}^{2} + {(v_{2})}^{2} + 2v_{1}v_{2} \cos( \theta) } = \sqrt{ {(v_{1})}^{2} + {(v_{2})}^{2} + 2v_{1}v_{2} \cos( 180 \degree - \theta) }$

Taking square on both sides :

$= > {(v_{1})}^{2} + {(v_{2})}^{2} + 2v_{1}v_{2} \cos( \theta) = {(v_{1})}^{2} + {(v_{2})}^{2} + 2v_{1}v_{2} \cos( 180 \degree - \theta)$

Cancelling the common terms:

$= > 2v_{1}v_{2} \cos( \theta) = 2v_{1}v_{2} \cos( 180 \degree - \theta)$

$= > \cos( \theta) = \cos(180 \degree - \theta)$

$= > \cos( \theta) = - \cos( \theta)$

$= > 2 \cos( \theta) = 0$

$= > \cos( \theta) = 0$

$= > \theta = 90 \degree$

So final answer:

Angle between the vectors is 90°

Answer 2

Answer: Here is your answer

Explanation: