Let u and v are unit vectors such that u-v-u-w and w-u-v- then the value of -u-v-w- is

The correct option is C 1 Given, u×v+u=w and w×u=v ⇒(u×v+u)×u=v ⇒(u×v)×u=v ⇒v (u.v)=v ⇒(u.v)u=0 ⇒(u.v)=0 Now , [uvw ...

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Byju's Answer

Standard XII

Mathematics

Scalar Triple Product

Let u and ...

Question

Let $\to u$ and $\to v$ are unit vectors such that $\to u \times \to v + \to u = \to w$ and $\to w \times \to u = \to v,$ then the value of $[\to u, \to v, \to w]$ is

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Solution

The correct option is C $1$
Given, $\to u \times \to v + \to u = \to w$ and $\to w \times \to u = \to v$
$\Rightarrow (\to u \times \to v + \to u) \times \to u = \to v$
$\Rightarrow (\to u \times \to v) \times \to u = \to v$
$\Rightarrow \to v - (\to u . \to v) = \to v$
$\Rightarrow (\to u . \to v) \to u = 0$
$\Rightarrow (\to u . \to v) = 0$
Now , $[\to u \to v \to w] = \to u . (\to v \times \to w)$
$= \to u . (\to v \times (\to u \times \to v + \to u))$
$= \to u . (\to v \times (\to u \times \to v) + \to v \times \to u)$
$= \to u . ({\to v}^{2} . \to u - (\to u . \to v) \to v + \to v \times \to u)$
$= {\to v}^{2} . {\to u}^{2} = 1$

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Let →u and →v are unit vectors such that →u×→v+→u=→w and →w×→u=→v, then the value of [→u,→v,→w] is

Let $\to u$ and $\to v$ are unit vectors such that $\to u \times \to v + \to u = \to w$ and $\to w \times \to u = \to v,$ then the value of $[\to u, \to v, \to w]$ is