Question

Find the magnitude of two vectors,a and b, having the same magnitude and such that the angle between them is 60° and their scalar product is. 1/2

Answer 1

required magnitude is 1. I use the definition of scalar product to come to the answer. Hope it helped

Answer 2

Answer:

The magnitude of both vectors is 1.

Step-by-step explanation:

Given the two vectors a and b having the same magnitude and such that the angle between them is 60° and their scalar product is $\frac{1}{2}$.

i.e  $|\vec{a}|=|\vec{b}|$

$\theta=60^{\circ}\\\\\vec{a}.\vec{b}=\frac{1}{2}\\\\\text{The dot product can be written as } \vec{a}.\vec{b}=|\vec{a}|.|\vec{b}|\cos\theta$

$\frac{1}{2}=|\vec{a}|.|\vec{b}|\cos 60\\\\\frac{1}{2}=|\vec{a}|.|\vec{a}|(\frac{1}{2})\\\\|\vec{a}|^2=1\\\\|\vec{a}|=1$

Hence,

$|\vec{a}|=|\vec{b}|=1$

The magnitude of both vectors is 1.