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Collinear Vectors

Let a, b be...

Question

Let $a, b$ be two noncollinear vectors. If $A = (x + 4 y) a + (2 x + y + 1) b$ $B = (y - 2 x + 2) a + (2 x - 3 y - 13) b$ and $3 A = 2 B$ , then $(x, y)$ $=$

(1, 2)

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(1, - 2)

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(2, - 1)

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(- 2, - 1)

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Solution

The correct option is C $(2, - 1)$
$3 A = 2 B$

$3 ((x + 4 y) a + (2 x + y + 1) b) = 2 ((y - 2 x + 2) a + (2 x - 3 y - 1) b)$

as $a$ & $b$ are not collinear

$(3 x + 12 y) a + (6 x + 3 y + 3) b = ((2 y - 4 x + 4) a + (4 x - 6 y - 2) b)$

$3 x + 12 y = 2 y - 4 x + 4$

$7 x + 10 y = 4$ -(1)

$6 x + 3 y + 3 = 4 x - 6 y - 2$

$2 x + 9 y = - 5$ -(2)

Solving (1) and (2) we get,

$x = 2$ $y = - 1$

Suggest Corrections

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