If a + b + c = 0, then which relation is correct - Vidyadip

MCQ

If $a + b + c = 0,$ then which relation is correct

A
$a = b = c = 0$
B
$a\,.\,b = b\,.\,c = c\,.\,a$
✓
$a \times b = b \times c = c \times a$
D
None of these

✓

Answer

Correct option: C.

$a \times b = b \times c = c \times a$

c
(c) Since $a + b + c = 0$

$ \Rightarrow a \times (a + b + c) = 0 \Rightarrow a \times a + a \times b + a \times c = 0$

$ \Rightarrow a \times b = - a \times c = c \times a$ .....$(i)$

Similarly, $b \times (a + b + c) = 0$$ \Rightarrow a \times b = b \times c$.....$(ii)$

By $(i)$ and $(ii),$ we get $a \times b = b \times c = c \times a.$

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