If u- v- w are three non-zero and non-coplanar vectors- then u-v-w-u-v- v-w - is equal to-

Let nbsp;(u+v w)·[(u v)× (v w )]=E ⇒ E=(u+v w)· nbsp; nbsp;[(u×v) (u×w) 0+(v×w)] Now, on multiplying (taking dot product) each term, we have: ⇒ E=u·v×w v· ...

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Byju's Answer

Standard XII

Mathematics

Linear Combination of Vectors

If u, v, w ar...

Question

If $\to u, \to v, \to w$ are three non-zero and non-coplanar vectors, then $(\to u + \to v - \to w) \cdot [(\to u - \to v) \times (\to v - \to w)]$ is equal to:

0

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\to u \cdot (\to v \times \to w)

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\to u \cdot (\to w \times \to v)

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3 \to u \cdot (\to v \times \to w)

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Solution

The correct option is B $\to u \cdot (\to v \times \to w)$
Let $(\to u + \to v - \to w) \cdot [(\to u - \to v) \times (\to v - \to w)] = E$
$\Rightarrow E = (\to u + \to v - \to w) \cdot [(\to u \times \to v) - (\to u \times \to w) - 0 + (\to v \times \to w)]$
Now, on multiplying (taking dot product) each term, we have:
$\Rightarrow E = \to u \cdot \to v \times \to w - \to v \cdot \to u \times \to w - \to w \cdot \to u \times \to v$
$\Rightarrow E = [\to u \to v \to w] + [\to u \to v \to w] - [\to u \to v \to w]$
$\Rightarrow E = \to u \cdot (\to v \times \to w)$

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Similar questions

Q. If

\to u, \to v

and

\to w

are three non-coplanar vectors, then

(\to u + \to v - \to w) . (\to u - \to v) \times (\to v - \to w)

equals

Q. If

\to u, \to v, \to w

are non-coplanar vectors and

p, q

are real numbers then the equality

[3 \to u p \to v p \to w] - [p \to v \to w q \to u] + [2 \to w q \to v q \to u] = 0

holds for

Q. If

\to u, \to v, \to w

are three noncoplanar vectors then

[\to u + \to v - \to w \to u - \to v \to v - \to w]

equals

Q. If

\to u, \to v, \to w

are non-coplanar vectors and

p, q

are real numbers, then the equality

[\begin{matrix} 3 \to u & p \to v & p \to w \end{matrix}] - [\begin{matrix} p \to v & q \to w & \to u \end{matrix}] - [\begin{matrix} 2 \to w & q \to v & q \to u \end{matrix}] = 0

holds for

Q. Let

\to u, \to v

and

\to w

be vectors such that

\to u + \to v + \to w = \to 0 .

| \to u | = 3, | \to v | = 4

and

| \to w | = 5,

then

\to u . \to v + \to v . \to w + \to w . \to u

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If →u,→v,→w are three non-zero and non-coplanar vectors, then (→u+→v−→w)⋅[(→u−→v)×(→v−→w)] is equal to:

If $\to u, \to v, \to w$ are three non-zero and non-coplanar vectors, then $(\to u + \to v - \to w) \cdot [(\to u - \to v) \times (\to v - \to w)]$ is equal to: