If a,b,c are three coplanar vectors, then [a + b , ,b + c , ,c + … - Vidyadip

MCQ

If $ a,b,c $ are three coplanar vectors, then $[a + b\,\,b + c\,\,c + a] = $

A
$[a b c]$
B
$2 [a b c]$
C
$3 [a b c]$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d) $[a + b\,\,b + c\,\,c + a]$$ = [a\,b\,c] + [a\,b\,a] + [a\,c\,c]$

$ + [a\,c\,a] + [b\,b\,c] + [b\,b\,a] + [b\,c\,c] + [b\,c\,a]$

$ = [a\,b\,c] + [b\,c\,a] = 2[a\,b\,c] = 0$, ($a,b,c $ are coplanar).

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