If a, b, c are mutually perpendicular unit vectors, then |a + b +… - Vidyadip

MCQ

If $a, b, c$ are mutually perpendicular unit vectors, then $|a + b + c|\,\, = $

✓
$\sqrt 3 $
B
$3$
C
$1$
D
$0$

✓

Answer

Correct option: A.

$\sqrt 3 $

a
(a) Three mutually perpendicular unit vectors $ = a$, $b$ and $c$.

Therefore $|a|\, = \,|b|\, = \,|c|\, = 1$ and $a.b = b.c = c.a = 0$.

We know that

$|a + b + c{|^2} = (a + b + c)\,.\,(a + b + c) = \,\,|a{|^2} + |b{|^2}$

$ + |c{|^2} + 2(a\,.\,b\,\, + b\,.\,c\, + c\,.\,a) = 1 + 1 + 1 + 0 = 3$

or $|a + b + c|\, = \sqrt 3 .$

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