The angle between the vectors 3 ,i + j + 2 ,k and 2 ,i - 2 ,j + 4… - Vidyadip

MCQ

The angle between the vectors $3\,i + j + 2\,k$ and $2\,i - 2\,j + 4\,k$ is

A
${\cos ^{ - 1}}\frac{2}{{\sqrt 7 }}$
✓
${\sin ^{ - 1}}\frac{2}{{\sqrt 7 }}$
C
${\cos ^{ - 1}}\frac{2}{{\sqrt 5 }}$
D
${\sin ^{ - 1}}\frac{2}{{\sqrt 5 }}$

✓

Answer

Correct option: B.

${\sin ^{ - 1}}\frac{2}{{\sqrt 7 }}$

b
(b) $\cos \theta = \frac{{3(2) + (1)( - 2) + 2(4)}}{{\sqrt {9 + 1 + 4} \sqrt {4 + 4 + 16} }}$$ = \frac{{12}}{{\sqrt {14} \sqrt {24} }} = \frac{6}{{\sqrt {14} \sqrt 6 }}$

$ \Rightarrow \cos \theta = \frac{{\sqrt 3 }}{{\sqrt 7 }} \Rightarrow \sin \theta = \frac{2}{{\sqrt 7 }}$ ==> $\theta = {\sin ^{ - 1}}\left( {\frac{2}{{\sqrt 7 }}} \right)$.

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