Vector Algebra Question 166
Question: If $ \mathbf{a}=2\mathbf{i}+\mathbf{k},\mathbf{b}=\mathbf{i}+\mathbf{j}+\mathbf{k} $ and $ \mathbf{c}=4\mathbf{i}-3\mathbf{j}+7\mathbf{k}. $ If $ \mathbf{d}\times \mathbf{b}=\mathbf{c}\times \mathbf{b} $ and $ \mathbf{d},.,\mathbf{a}=0, $ then d will be
[IIT 1990]
Options:
A) $ \mathbf{i}+8\mathbf{j}+2\mathbf{k} $
B) $ \mathbf{i}-8\mathbf{j}+2\mathbf{k} $
C) $ -\mathbf{i}+8\mathbf{j}-\mathbf{k} $
D) $ -\mathbf{i}-8\mathbf{j}+2\mathbf{k} $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \mathbf{d}\times \mathbf{b}=\mathbf{c}\times \mathbf{b} $ gives $ | ,\begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ x & y & z \\ 1 & 1 & 1 \\ \end{matrix}, |=| ,\begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 4 & -3 & 7 \\ 1 & 1 & 1 \\ \end{matrix}, |,, $ where $ \mathbf{d}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k} $ (say)
On solving, $ x=-1, $ $ y=-8, $ $ z=2 $
Hence $ \mathbf{d}=-\mathbf{i}-8\mathbf{j}+2\mathbf{k}. $
BETA
