Given three unit vector a, ,b, ,c such that a , ,b and a||b , the… - Vidyadip

MCQ

Given three unit vector $a,\,b,\,c$ such that $a\, \bot \,b$ and $a||b$ , then $a\times (b\times c)$ is

A
$a$
✓
$b$
C
$c$
D
$0$

✓

Answer

Correct option: B.

$b$

b
(b) $a\times (b\times c)=(a\,.\,c)\,b-(a\,.\,b)\,c$

$\because \,\,a\, \bot \,\,b\,\,,\,\,\,\therefore \,\,\,a\,.\,b = 0$

$\because a|\,|c$, $\therefore \,\,\,a\,.\,c = 1$ $(a, b$ and $ c $ are unit vectors)

$a \times (b \times c) = (1)b - (0)\,c\,$=$ b.$

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