Mathematics · Vector Algebra

JEE Main 2024 — 29 January, Shift 1 — Question 7

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 $\vec{a}+\alpha \vec{b}+\beta \vec{c}=\overrightarrow{0}$ , then $\alpha+\beta$ is equal to

Option A:
35
Correct
Option B:
30
Option C:
-30
Option D:
-25

Answer: A

Step-by-step solution

$\vec{a}+5 \vec{b}=\lambda \vec{c}$

$\overrightarrow{\mathrm{b}}+6 \overrightarrow{\mathrm{c}}=\mu \overrightarrow{\mathrm{a}}$

Eliminating $\vec{a}$

$\lambda \overrightarrow{\mathrm{c}}-5 \overrightarrow{\mathrm{~b}}=\frac{6}{\mu} \overrightarrow{\mathrm{c}}+\frac{1}{\mu} \overrightarrow{\mathrm{~b}}$

$\therefore \mu=\frac{-1}{5}, \lambda=-30$

$\alpha=5, \beta=30$

$\alpha+\beta=35$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 29 January, Shift 1
Subject: Mathematics
Chapter: Vector Algebra
Topic: Linear Independence and Dependence of Vectors

Let O be the origin and the position vector of A and B be 2 hati+2 hatj+hatk and 2 hati+4 hatj+4 hatk respectively. If the internal…

Answer: A

Step-by-step solution

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