If a- b- c-a- b- c- where a- b -c are any three vectors such that a- b 0- c 0- then a- c are -

Explanation for correct option:Given, a× (b× c)=(a× b)× c,Also we know that, a× (b× c)=(a.c)b (b.a)c &0ex0ex(a× b)× c=(a.c)b (c.b)aNow, using the ...

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Byju's Answer

Standard XII

Mathematics

Continuity of a Function

If a× b× c=a×...

Question

If $a \times (b \times c) = (a \times b) \times c$ , where $a, b, c$ are any three vectors such that $a ∙ b \neq 0, c \neq 0$ , then $a, c$ are $?$

Inclined at an angle of $\frac{π}{6}$ between them

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Perpendicular

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Parallel

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$\frac{π}{3}$ Inclined at angle of between them

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Solution

The correct option is C
Parallel

Explanation for correct option:
Given, $a \times (b \times c) = (a \times b) \times c$ ,
Also we know that,
$a \times (b \times c) = (a . c) b - (b . a) c & (a \times b) \times c = (a . c) b - (c . b) a$
Now, using the above formulae,
$\begin{array}{rcl} (a \times b) \times c & = & a \times (b \times c) \\ \Rightarrow & (a . c) b - (b . c) a = (a . c) b - (a . b) c \\ \Rightarrow (b . c) a & = & (a . b) c \end{array}$
$\begin{array}{rcl} (b . c) a n d (a . b) a r e s c a l a r \end{array}$
Therefore, $a$ parallel to $c$
Hence, the correct option is (C).

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If a×(b×c)=(a×b)×c, where a,b,c are any three vectors such that a∙b≠0,c≠0, then a,c are ?

If $a \times (b \times c) = (a \times b) \times c$ , where $a, b, c$ are any three vectors such that $a ∙ b \neq 0, c \neq 0$ , then $a, c$ are $?$