Question

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

• A. 0
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

3

Answer 2

Let $\vec { A } = 2 \hat { i } + 3 \hat { j } - \hat { k }$ and $\vec { B } = - 4 \hat { i } - 6 \hat { j } + \lambda \hat { k }$

$\frac { a _ { 1 } } { b _ { 1 } } = \frac { a _ { 2 } } { b _ { 2 } } = \frac { a _ { 3 } } { b _ { 3 } }$ i.e. $\frac { 2 } { - 4 } = \frac { 3 } { - 6 } = \frac { - 1 } { \lambda }$ $\Rightarrow \lambda = 2$.