Question

If the position vectors of A, B, C, D are $2\mathbf{i} + \mathbf{j},$ $\mathbf{i} - 3\mathbf{j},$ $3\mathbf{i} + 2\mathbf{j}$ and $\mathbf{i} + \lambda\mathbf{j}$ respectively and $\overset{\rightarrow}{AB}||\overset{\rightarrow}{CD}$ , then $\lambda$ will be

• A. – 8
• B. – 6
• C. 8
• D. 6

Answer 1

Answer: (B)

– 6

Answer 2

$\overset{\rightarrow}{AB} = - \mathbf{i} - 4\mathbf{j},$ $\overset{\rightarrow}{CD} = - 2\mathbf{i} + (\lambda - 2)\mathbf{j}$

$\because\overset{\rightarrow}{AB}||\overset{\rightarrow}{CD}$. So ,$\frac{- 1}{- 2} = \frac{- 4}{\lambda - 2}$, $\lambda - 2 = - 8$ or $\lambda = - 6.$