Question

if the magnitude of the resultant of two vectors equal of magnitude is equal to the magnitude of either of the vector what is the angle between them​

Answer 1

Answer:

See below.

Explanation:

Let a, b and c be the vectors. Here, c is the resultant vector of a and b.

So, the magnitude of vector c could be assumed to be equal to the magnitude of vector b.

$| \vec{c} | = | \vec{b} |$

We know,

$|\vec{c}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + 2|\vec{a}||\vec{b}|\cos(\theta)$

Assuming the magnitude of vector c to be equal to the magnitude of vector b,

$0 = |\vec{a}|^2 + 2|\vec{a}||\vec{b}|\cos(\theta)\\\frac{- |\vec{a}|^2}{2|\vec{a}||\vec{b}|} = \cos(\theta)\\\cos( \theta ) = \frac{ - |\vec{a}| }{ 2 |\vec{b}|}$

That should be the final equation.