Question

the angle between two vectors of equal magnitude is p, the magnitude of the resultant vector is​

Answer 1

$\mathfrak{\large{\underline{\underline{Given:-}}}}$

The angle between two vector is p.

$\mathfrak{\large{\underline{\underline{To find:-}}}}$

The magnitude of the resultant vector.

$\mathfrak{\large{\underline{\underline{Solution:-}}}}$

Let the two vectors A and B of equal magnitude and angle between two vector is P.

The resultant of vector is given by :-

$\boxed{\sf{ r = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos(p) } }}$

Where, p is angle between two vectors.

Also,

${a}^{→} = {b}^{→}$

Now,

$r = \sqrt{ {a}^{2} + {a}^{2} + 2aa \: cosp }$

$r = \sqrt{2 {a}^{2} + 2 {a}^{2} cosp }$

$r = \sqrt{2 {a}^{2}(1 + cosp) }$

$r = \sqrt{4 {a}^{2} {cos}^{2} \frac{p}{2} }$

$r = 2a \: \cos( \frac{p}{2} )$

hence, magnitude of resultant vector is = 2a Cos(P/2)

we can also write ,

Magnitude of resultant vector is = 2b Cos (p/2)

Formula used :-

Cos(p) = 2 cos² p/2 -1 .