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Addition of Vectors

OA = a , OC =...

Question

$- - \to O A = \to a, - - \to O C = \to b, - - \to O B = 10 \to a + 2 \to b$ where O, A, C are non-collinear points. Let $p$ denote the area of quadrilateral OABC & $q$ denote the area of parallelogram with OA and OC as adjacent sides. If $p = λ q$ , then $λ$ is

A

3

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B

5

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C

6

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D

8

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Solution

The correct option is C 6

$q = | \to a \times \to b |$
$p = A r (Δ O A B) + A r (Δ O B C)$
$= \frac{1}{2} {| \to a \times (10 \to a + 2 \to b) | + | \to b \times (10 \to a + 2 \to b) |}$
$= \frac{1}{2} {| 2 (\to a \times \to b) | + | 10 (\to b \times \to a) |}$
$p = 6 | \to a \times \to b |$
$∴ p = 6 q \Rightarrow λ = 6$

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