If a, b, c are non-zero vectors such that a , ,. , ,b = a , ,. , … - Vidyadip

MCQ

If $ a, b, c$ are non-zero vectors such that $a\,\,.\,\,b = a\,\,.\,\,c,$ then which statement is true

A
$b = c$
B
$a\, \bot \,(b - c)$
✓
$b = c$ or $a\, \bot \,(b - c)$
D
None of these

✓

Answer

Correct option: C.

$b = c$ or $a\, \bot \,(b - c)$

c
(c) $a.b = a.c \Rightarrow a.b - a.c = 0 \Rightarrow a.(b - c) = 0$

$ \Rightarrow $Either $b - c = 0\,\,{\rm{or}}\,\,a = 0 \Rightarrow b = c$ or $a \bot (b - c).$

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