Mathematics | VITEEE 2014 | Discussion Page

If $r= \alpha b \times c+\beta c \times a+ \gamma a \times b$ and [a b c]=2 , then $\alpha+\beta+\gamma$ is equal to

A) $r.[b \times c+c \times a+a \times b]$

B) $\frac{1}{2}r.(a+b+c)$

C) $2r.(a+b+c)$

D) 4

Option B

$r.a= \alpha( a.b \times c)+\beta(a.c \times a)+\gamma(a.a \times b)$

$=\alpha[abc]+0+0$ Similarly

$r.b=\beta [a bc]$ and $r.c=\gamma [abc]$

$\therefore$ $\frac{1}{2} r.(a+b+c)=\frac{1}{2} (r.a+r.b+r.c)$

$\frac{1}{2} (\alpha+\beta+\gamma)[abc]$

=$\frac{1}{2}(\alpha+\beta+\gamma)\times 2=\alpha+\beta+\gamma$

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