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Pascal Triangle

a=2i+k,b=3j+4...

Question

$¯ ¯ ¯ a = 2 ¯ i + ¯ ¯ ¯ k, ¯ ¯ b = 3 ¯ j + 4 ¯ ¯ ¯ k, ¯ ¯ c = 8 ¯ i - 3 ¯ j$ and $¯ ¯ ¯ a$ is expressed as a linear combination of $¯ ¯ b$ and $¯ ¯ c$ then $¯ ¯ ¯ a =$

A

\frac{1}{2} (¯ ¯ b + ¯ ¯ c)

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B

\frac{1}{3} (¯ ¯ b + ¯ ¯ c)

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C

\frac{1}{4} (¯ ¯ b + ¯ ¯ c)

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D

\frac{1}{4} (¯ ¯ b - ¯ ¯ c)

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Solution

The correct option is C $\frac{1}{4} (¯ ¯ b + ¯ ¯ c)$
$\to b + \to c$ $= (3 j + 4 k) + (8 i - 3 j)$
$= 8 i + 4 k$
$= 4 (2 i + k)$
$= 4 \to a$
Therefore $\to b + \to c = 4 (\to a)$
$∴ \frac{\to b + \to c}{4} = \to a$

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