Let p- q- r- be three mutually perpendicular vectors of the same magnitude- If a vector x- satisfies the equation- p-x-q-p-q-x-r-q-r-x-p-r-0- then x- is given by1-2-p-q-2r-1-2-p-q-r-1-3-p-q-r-1-3-2p-q-r-

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Orthogonal System of Vectors

Let p⃗, q⃗, r...

Question

Let $\to p, \to q, \to r$ be three mutually perpendicular vectors of the same magnitude. If a vector $\to x$ satisfies the equation
$\to p [(\to x - \to q) \times \to p] + \to q \times [(\to x - \to r) \times \to q] + \to r \times [(\to x - \to p) \times \to r] = \to 0$ , then $\to x$ is given by

\frac{1}{2} (\to p + \to q - 2 \to r)

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\frac{1}{2} (\to p + \to q + \to r)

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\frac{1}{3} (\to p + \to q + \to r)

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\frac{1}{3} (2 \to p + \to q - \to r)

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Solution

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Similar questions

\to p, \to q, \to r

\to x

\to p [(\to x - \to q) \times \to p] + \to q \times [(\to x - \to r) \times \to q] + \to r \times [(\to x - \to p) \times \to r] = \to 0

\to x

\to p, \to q, \to r

\to x

\to p \times ((\to x - \to q) \times \to p) + \to q \times ((\to x - \to r) \times \to q) + \to r \times ((\to x - \to p) \times \to r) = 0

\to p, \to q, \to r

\to x

\to p \times {(\to x - \to q) \times \to p} + \to q \times {(\to x - \to r) \times \to q} + \to r \times {(\to x - \to p) \times \to r}

[\to p + 2 \to q + 3 \to r \to q + 2 \to r + 3 \to p \to r + 2 \to p + 3 \to q] = 54

\to p

\to q

\to r

∣ ∣ ∣ ∣ \begin{matrix} \to p . \to p & \to p . \to q & \to p . \to r \to p . \to q & \to q . \to q & \to q . \to r \to p . \to r & \to r . \to q & \to r . \to r \end{matrix} ∣ ∣ ∣ ∣

\to x

[\to p \to q \to r] \to x = (\to p \times \to q) \times \to r,

\to x

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