Vector Algebra Question 6
Question 6 - 2024 (29 Jan Shift 1)
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 $\overrightarrow{c}, \overrightarrow{b}+6 \overrightarrow{c}$ is collinear with $\overrightarrow{a}$ and $\overrightarrow{a}+\alpha \overrightarrow{b}+\beta \overrightarrow{c}=\overrightarrow{0}$, then $\alpha+\beta$ is equal to
(1) 35
(2) 30
(3) -30
(4) -25
Show Answer
Answer (1)
Solution
$\vec{a}+5 \vec{b}=\lambda \vec{c}$
$\vec{b}+6 \vec{c}=\mu \vec{a}$
Eliminating $\vec{a}$
$\lambda \overrightarrow{c}-5 \overrightarrow{b}=\frac{6}{\mu} \overrightarrow{c}+\frac{1}{\mu} \overrightarrow{b}$
$\therefore \mu=\frac{-1}{5}, \lambda=-30$
$\alpha=5, \beta=30$
