The angle between two vectors given by 6 i+6 j-3 k and 7 i+4 j+4 … - Vidyadip

MCQ

The angle between two vectors given by $6 \bar{i}+6 \bar{j}-3 \bar{k}$ and $7 \bar{i}+4 \bar{j}+4 \bar{k}$ is

A
$\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
B
$\cos ^{-1}\left(\frac{5}{\sqrt{3}}\right)$
C
$\sin ^{-1}\left(\frac{2}{\sqrt{3}}\right)$
✓
$\sin ^{-1}\left(\frac{\sqrt{5}}{3}\right)$

✓

Answer

Correct option: D.

$\sin ^{-1}\left(\frac{\sqrt{5}}{3}\right)$

(d)$\begin{aligned}& \cos \theta=\frac{\vec{A} \vec{B}}{A B}=\frac{42+24-12}{\sqrt{36+36+9} \sqrt{49+16+16}}=\frac{56}{9 \sqrt{71}} \\\cos \theta=\frac{56}{9 \sqrt{71}} \therefore \sin \theta=\frac{\sqrt{5}}{3} \text { or } \theta=\sin ^{-1}\left(\frac{\sqrt{5}}{3}\right)\end{aligned}$

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