The angle between the vector a = 2i + 3j + k and b = 2i - j - k i… - Vidyadip

MCQ

The angle between the vector $a = 2i + 3j + k$ and $b = 2i - j - k$ is

✓
$\pi /2$
B
$\pi /4$
C
$\pi /3$
D
$0$

✓

Answer

Correct option: A.

$\pi /2$

a
(a) Let $a = 2i + 3j + k$ and $b = 2i - j - k$

Since $\cos \,\theta = \frac{{a\,.b}}{{|a||b|}}$

$ = \frac{{(2i + 3j + k)\,.\,(2i - j - k)\,}}{{\sqrt {{{(2)}^2} + {{(3)}^2} + {{(1)}^2}} \sqrt {{{(2)}^2} + {{( - 1)}^2} + {{( - 1)}^2}} }}$

$ = \frac{{4 - 3 - 1}}{{\sqrt {(4 + 9 + 1)} \sqrt {(4 + 1 + 1)} }} = 0$

$\therefore \theta = \frac{\pi }{2}$.

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