Given three non-zero- non-coplanar vectors a- b- and c- r-1- - pa- - qb- - c- and r-2- - a- - pb- - qc- If the vectors r-1- - 2r-2- and 2r-1- r-2- are collinear- then p- q is

The correct option is D (1, 1) r⃗_⃗1⃗ + 2r⃗_⃗2⃗ = (p nbsp;a⃗ + qb⃗ + nbsp;c⃗) + 2(a⃗ + pb⃗ + qc⃗)=(p + 2) nbsp;a⃗ + nbsp;(q + 2p) nbsp;b⃗ + ...

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Test for Collinearity of Vectors

Given three n...

Question

Given three non-zero, non-coplanar vectors $\to a, \to b$ and $\to c$ . $_{1} = p \to a + q \to b + \to c$ and $_{2} = \to a + p \to b + q \to c$ . If the vectors $_{1} + 2_{2}$ and $2_{1} +_{2}$ are collinear, then $(p, q)$ is

(0, 0)

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(1, - 1)

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(- 1, 1)

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(1, 1)

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Solution

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Similar questions

\to a

\to b

\to c

_{1} = p \to a + q \to b + \to c

_{2} = \to a + p \to b + q \to c

_{1} + 2_{2}

2_{1} +_{2}

(p, q)

\to a, \to b, \to c

_{1} = \to a - \to b + \to c,_{2} = \to b + \to c - \to a

_{3} = \to c + \to a - \to b, \to r = 2 \to a - 2 \to b + 4 \to c

\to r = x_{1}_{1} + x_{2}_{2} + x_{3}_{3}

\to a, \to b, \to c

_{1} = \to a - \to b + \to c,_{2} = \to b + \to c - \to a

_{3} = \to c + \to a + \to b, \to r = 2 \to a - 3 \to b + 4 \to c

\to r = λ_{1}_{1} + λ_{2}_{2} + λ_{3}_{3}

\to a, \to b, \to c

_{1} = \to a - \to b + \to c,_{2} = \to b + \to c - \to a,_{3} = \to c + \to a + \to b

\to r = 2 \to a - 3 \to b + 4 \to c

\to r = λ_{1}_{1} + λ_{2}_{2} + λ_{3}_{3}

\to a, \to b, \to c

{\to a \times (\to b + \to c)} \times {\to b \times (\to c - \to a)}

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