Question

please please please please solve it​

Answer 1

Question:

$\sf{Find\:\left(|\vec{a_1}-\vec{a_2|}\right)\left(2\vec{a_1}+\vec{a_2}\right)}$

Solution:

$\sf{|\vec{a_1}|=a_1=1}\\\sf{|\vec{a_2}|=a_2=1}$

$\sf{\left(|\vec{a_1}+\vec{a_2}|\right)^2=\left(\sqrt{3}\right)^2}$

$\sf{a_1^2+a_2^2+2\vec{a_1}.\vec{a_2}=3}$

$\sf{Now,a_1=a_2=1}$

$\sf{Therefore,\vec{a_1}.\vec{a_2}=\dfrac{1}{2}}$

$\sf{So,\left(\vec{a_1}-\vec{a_2}\right)\left(2\vec{a_1}+\vec{a_2}\right)}$

$\sf{2a_1^2+\vec{a_1}.\vec{a_2}-2\vec{a_1}.\vec{a_2}-a_2^2}$

$\sf{2-\dfrac{1}{2}-1}$

$\sf{1-\dfrac{1}{2}}$

$\boxed{\sf{\dfrac{1}{2}}}$