Question

If A=B-C then dertamine angle between A and B

Answer 1

$\textbf{Given:}$

$\vec{a}=\vec{b}-\vec{c}$

$\textbf{To find:}$

$\text{The angle between \vec{a} and \vec{b} }$

$\textbf{Solution:}$

$\text{Assume that \vec{a} , \vec{b} and \vec{c} are unit vectors}$

$\text{Consider,}$

$\vec{a}=\vec{b}-\vec{c}$

$\vec{a}-\vec{b}=-\vec{c}$

$\text{Taking modulus on bothsides, we get}$

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

$|\vec{a}-\vec{b}|^2=|-\vec{c}|^2$

$|\vec{a}|^2+|\vec{b}|^2-2\,\vec{a}.\vec{b}=|\vec{c}|^2$

$|\vec{a}|^2+|\vec{b}|^2-2\,|\vec{a}|\,|\vec{b}|\,cos\,\theta=|\vec{c}|^2$

$1^2+1^2-2(1)(1)\,cos\,\theta=1^2$

$2-2\,cos\,\theta=1$

$-2\,cos\,\theta=-1$

$cos\,\theta=\dfrac{1}{2}$

$\implies\bf\theta=60^{\circ}$

$\textbf{Answer:}$

$\textbf{The angle between \bf\vec{a} and \bf\vec{b} is \bf\,60^{\circ} }$

Answer 2

Answer:. -> ->

The angle between A and B is 60°