Discussion Forum

 if  $a=\hat{i}-\hat{j}+2\hat{k}$   and  $b=2\hat{i}-\hat{j}+\hat{k}$ , then the angle $\theta$ between a and b s given by

Answer:

Explanation:

$\cos\theta=\frac{a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}}{\sqrt{a^{2}_{1}+a^{2}_{2}+a^{2}_{}}\sqrt{b^{2}_{1}+b^{2}_{2}+b^{2}_{3}}}$

$=\frac{1\times2+(-1)\times(-1)+2\times(1)}{\sqrt{1+1+4}\sqrt{4+1+1}}$

$\frac{2+2+2}{6}=\frac{6}{6}=1$

 So, $\theta$ = 0°  or $\theta$= 2$\pi$

 $\because sec 2\pi=1$

$\therefore$     $2\pi=\sec^{-1}(1)$

$\Rightarrow \theta  =\sec^{-1}(1)$