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

The correct option is A Parallel. (a̅×b̅ )×c̅ =a̅× (b̅×c̅ ) (c̅·a̅ )b̅ (c̅·b̅ )a̅ =(a̅·c̅ )b̅ (a̅·b̅ )c̅ 2(a⃗·c⃗)b⃗=(c⃗·b⃗)a⃗ (a⃗·b⃗)c⃗ b⃗ ...

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Byju's Answer

Standard XII

Mathematics

Section Formula

If a⃗×b⃗ ×c...

Question

If $(\to a \times \to b) \times \to c = \to a \times (\to b \times \to c),$ are any three vectors such that $\to a \cdot \to b \neq 0, \to b \cdot \to c \neq 0$ then $\to a$ and $\to b$ are

Inclined at an angle of

\frac{π}{3}

between them

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Inclined at an angle of

\frac{π}{6}

between them

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Perpendicular

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Parallel.

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Solution

The correct option is A Parallel.
$(¯ a \times ¯ b) \times ¯ c = ¯ a \times (¯ b \times ¯ c)$
$(¯ c \cdot ¯ a) ¯ b - (¯ c \cdot ¯ b) ¯ a = (¯ a \cdot ¯ c) ¯ b - (¯ a \cdot ¯ b) ¯ c$
$2 (\to a \cdot \to c) \to b = (\to c \cdot \to b) \to a - (\to a \cdot \to b) \to c$
$\to b = \frac{(\to c \cdot \to b)}{2 (\to a \cdot \to c)} \to a + (- \frac{(\to a \cdot \to b}{2 (\to a \cdot \to c)}) \to c$
Let scalar quantity is constant
$\to b = λ \to a + μ \to c$
Hence $¯ a, ¯ c$ are parallel. to $\to b$

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