Vector Algebra Question 192
Question: If $ \mathbf{x} $ is parallel to $ \mathbf{y} $ and $ \mathbf{z} $ where $ \mathbf{x}=2\mathbf{i}+\mathbf{j}+\alpha \mathbf{k} $ , $ \mathbf{y}=\alpha \mathbf{i}+\mathbf{k} $ and $ \mathbf{z}=5\mathbf{i}-\mathbf{j} $ , then $ \alpha $ is equal to
[J & K 2005]
Options:
A) $ \pm \sqrt{5} $
B) $ \pm \sqrt{6} $
C) $ \pm \sqrt{7} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- Given x is parallel to y and z
$ \therefore $ $ \mathbf{x},.,(\mathbf{y}\times \mathbf{z})=0 $
$ \Rightarrow $ $ [\mathbf{x}\mathbf{y}\mathbf{z}]=0 $
Þ $ | ,\begin{matrix} 2 & 1 & \alpha \\ \alpha & 0 & 1 \\ 5 & -1 & 0 \\ \end{matrix}, |=0\Rightarrow \alpha =\pm ,\sqrt{7} $ .
BETA
