Vectors a- b- c - b- c- a and c- a- b are

The correct option is B linearly dependent vectors a×( b× c ) +b×( c× a ) +c×( a× b ) =( a.c ) b ( a.b ) c+( b.a ) c ( b.c ) a+( c.b ) a ( c.a ) b=0 ...

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Byju's Answer

Standard XII

Mathematics

Equal Vectors

Vectors a× ...

Question

Vectors $a \times (b \times c), b \times (c \times a)$ and $c \times (a \times b)$ are

linearly dependent vectors

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equal vectors

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parallel vectors

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none of these

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Solution

The correct option is B linearly dependent vectors
$a \times (b \times c) + b \times (c \times a) + c \times (a \times b) = (a . c) b - (a . b) c + (b . a) c - (b . c) a + (c . b) a - (c . a) b = 0$
$∴$ The given vectors are linearly dependent.

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Vectors a×(b×c), b×(c×a) and c×(a×b) are

The correct option is B linearly dependent vectorsa×(b×c)+b×(c×a)+c×(a×b)=(a.c)b−(a.b)c+(b.a)c−(b.c)a+(c.b)a−(c.a)b=0∴ The given vectors are linearly dependent.

Vectors $a \times (b \times c), b \times (c \times a)$ and $c \times (a \times b)$ are

The correct option is B linearly dependent vectors
$a \times (b \times c) + b \times (c \times a) + c \times (a \times b) = (a . c) b - (a . b) c + (b . a) c - (b . c) a + (c . b) a - (c . a) b = 0$
$∴$ The given vectors are linearly dependent.