The value of a-b - b-c - c-a - is

The correct option is C 0 The given value =( a b ) .( b× c b× a c× c+c× a ) =( a b ) ( b× c+c× a+a× b ) =a.( b× c ) +0+0 0 0 b.( c× a ) ...

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Standard XII

Mathematics

Purely Real

The value of ...

Question

The value of $(a - b) . [(b - c) \times (c - a)]$ is

2 [a b c]

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3 [a b c]

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0

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None of these

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Solution

The correct option is C $0$
The given value
$= (a - b) . (b \times c - b \times a - c \times c + c \times a) = (a - b) (b \times c + c \times a + a \times b) = a . (b \times c) + 0 + 0 - 0 - 0 - b . (c \times a) = [a b c] - [b c a] = 0 [∵ [a b c] = [b c a]]$

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The value of (a−b).[(b−c)×(c−a)] is

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The value of $(a - b) . [(b - c) \times (c - a)]$ is

The correct option is C $0$
The given value
$= (a - b) . (b \times c - b \times a - c \times c + c \times a) = (a - b) (b \times c + c \times a + a \times b) = a . (b \times c) + 0 + 0 - 0 - 0 - b . (c \times a) = [a b c] - [b c a] = 0 [∵ [a b c] = [b c a]]$