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Applications Scalar Triple Product

Let a=-î+4k̂,...

Question

Let $\to a = -^i + 4^k, \to b = 5^i + 2^k$ and $\to c = - 3^i +^k .$ If $\to a = x \to b + y \to c,$ then the value of $(x, y)$ is

A

(1, 1)

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B

(- 2, 2)

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C

(1, 2)

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D

(2, - 1)

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Solution

The correct option is C $(1, 2)$
Given :
$\to a = x \to b + y \to c$
$\Rightarrow -^i + 4^k = x (5^i + 2^k) + y (- 3^i +^k)$
Equating the cofficient of like vectors, we get
$\Rightarrow 5 x - 3 y = - 1 \dots (i) 2 x + y = 4 \dots (i i)$
Solving $(i)$ and $(i i),$ we get
$x = 1, y = 2$

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Applications Scalar Triple Product

Standard XII Mathematics

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