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Angle between Two Planes

Given that th...

Question

Given that the vectors $\to a$ and $\to b$ are non-collinear. The values of $x$ and $y$ for which the vector equality $2 \to u - \to v = \to w$ holds true if

A

x = 2, y = 1

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B

x = 1, y = 2

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C

x = - 2, y = 1

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D

x = - 2, y = - 1

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Solution

The correct option is A $x = 2, y = 1$
$\to u = 2 x \to α + y \to β, \to v = 2 y \to α + 3 x \to β, \to w = 2 \to α - 5 \to β \to u - \to v = \to w ⟹ (2 x \to α + y \to β) - (2 y \to α + 3 x \to β) = 2 \to α - 5 \to β ⟹ 2 (x - y) \to α + (y - 3 x) \to β = 2 \to α - 5 \to β ⟹ 2 (x - y) = 2, y - 3 x = - 5$
Solving the equations we get $x = 2, y = 1$
Hence, A is correct.

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