Question

If two vectors $2\widehat{i} + 3\widehat{j} - \widehat{k}$ and $- 4\widehat{i} - 6\widehat{j} - \lambda\widehat{k}$ are parallel to each other then value of λ be.

• A. 0
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

2

Answer 2

Let $\overset{\rightarrow}{A} = 2\widehat{i} + 3\widehat{j} - \widehat{k}$ and $\overset{\rightarrow}{B} = - 4\widehat{i} - 6\widehat{j} + \lambda\widehat{k}$

$\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B}$ are parallel to each other

$\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}} = \frac{a_{3}}{b_{3}}$ i.e. $\frac{2}{- 4} = \frac{3}{- 6} = \frac{- 1}{\lambda} \Rightarrow \lambda = 2$.