Question

10)
The sum of two vectors of equal magnitudes is a vector of magnitude equal to either of the
vector. The angle between the vectors is

Answer 1

Answer:

90°

Explanation:-

The angle between the vectors is90°

Answer 2

Answer:  $\theta = 120^0$

Explanation:

Let the two vectors are $\vec A ~ \& ~ \vec B$ whose magnitudes are equal i.e. $|A| ~ = ~ | B|$ .

It is given that, the sum of these two vectors is a vector of magnitude equal to either of the vector i.e.

$|\vec A + \vec B |= |\vec A|$  

Squaring the both sides,

$(\vec A + \vec B) . (\vec A + \vec B) = \vec A . \vec A\\\\or, | A |^2 + |B|^2 + 2 |A| |B| cos\theta = |A|^2\\\\or, |B|^2 + 2 |B|^2 cos\theta = 0\\\\or, |B|^2 ( 1 +2 cos\theta) = 0$

Since $|B| \neq 0$

$(1+2cos\theta) = 0\\\\or, cos\theta = -1/2 \\\\or, \theta = 120^0$

So, the angle between the vectors is $120^0$.