QJEEM24Ma65b3: JEE Main 2024 Physics - Class 11 JEEM24Ma65b3 Solution: Let a → , b → and c → be three non-zero vectors such that b →…

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QJEEM24Ma65b3: JEE Main 2024 Physics - Class 11 JEEM24Ma65b3 Solution: Let a → , b → and c → be three non-zero vectors such that b →…

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that $\vec{b}$ and $\vec{c}$ are non-collinear. If $\vec{a} + 5 \vec{b}$ is collinear with $\vec{c}, \vec{b} + 6 \vec{c}$ is collinear with $\vec{a}$ and $\vec{a} + α \vec{b} + β \vec{c} = \vec{0}$ , then $α + β$ is equal to

Multiple Choice Options

A 30
B −30
C −25
D 35

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Accepted Answer

$\begin{aligned} \vec{a} + 5 \vec{b} = λ \vec{c} \\ \vec{b} + 6 \vec{c} = μ \vec{a} \end{aligned}$

Eliminating $\vec{a}$

$\begin{aligned} λ \vec{c} - 5 \vec{b} = \frac{6}{μ} \vec{c} + \frac{1}{μ} \vec{b} \\ ∴ μ = \frac{- 1}{5}, λ = - 30 \\ α = 5, β = 30 \end{aligned}$

QJEEM24Ma65b3: JEE Main 2024 Physics - Class 11 JEEM24Ma65b3 Solution: Let a → , b → and c → be three non-zero vectors such that b →…

Multiple Choice Options

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