QJEEM24Mad2cb: JEE Main 2024 Physics - Class 11 JEEM24Mad2cb Solution: Let O A → = a → , O B → = 12 a → + 4 b →  and  O C →…

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QJEEM24Mad2cb: JEE Main 2024 Physics - Class 11 JEEM24Mad2cb Solution: Let O A → = a → , O B → = 12 a → + 4 b →  and  O C →…

Let $\vec{O A} = \vec{a}, \vec{O B} = 12 \vec{a} + 4 \vec{b} and \vec{O C} = \vec{b}$ , where O is the origin. If S is the parallelogram with adjacent sides OA and OC, then $\frac{area of the quadrilateral OA BC}{area of S}$ is equal to _________.

Multiple Choice Options

A 7
B 6
C 8
D 10

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Accepted Answer

JEE Main 2024 (Online) 29th January Evening Shift Mathematics - Vector Algebra Question 37 English Explanation

Area of parallelogram, $S = | \vec{a} \times \vec{b} |$

Area of quadrilateral $= Area (△ OAB) + Area (△ OBC)$

$\begin{aligned} = \frac{1}{2} {| \vec{a} \times (12 \vec{a} + 4 \vec{b}) | + | \vec{b} \times (12 \vec{a} + 4 \vec{b}) |} \\ = 8 | (\vec{a} \times \vec{b}) | \end{aligned}$

$Ratio = \frac{8 | (\vec{a} \times \vec{b}) |}{| (\vec{a} \times \vec{b}) |} = 8$

QJEEM24Mad2cb: JEE Main 2024 Physics - Class 11 JEEM24Mad2cb Solution: Let O A → = a → , O B → = 12 a → + 4 b → &nbsp;and&nbsp; O C →…

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QJEEM24Mad2cb: JEE Main 2024 Physics - Class 11 JEEM24Mad2cb Solution: Let O A → = a → , O B → = 12 a → + 4 b → and O C →…