Vector Algebra Question 199
Question: The point of intersection of $ \mathbf{r}\times \mathbf{a}=\mathbf{b}\times \mathbf{a} $ and $ \mathbf{r}\times \mathbf{b}=\mathbf{a}\times \mathbf{b} $ , where $ \mathbf{a}=\mathbf{i}+\mathbf{j} $ and $ \mathbf{b}=2\mathbf{i}-\mathbf{k} $ is
[Orissa JEE 2004]
Options:
A) $ 3\mathbf{i}+\mathbf{j}-\mathbf{k} $
B) $ 3\mathbf{i}-\mathbf{k} $
C) $ 3\mathbf{i}+2\mathbf{j}+\mathbf{k} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- We have $ \mathbf{r}\times \mathbf{b}=\mathbf{a}\times \mathbf{b} $ and $ \mathbf{r}\times \mathbf{a}=\mathbf{b}\times \mathbf{a} $
Adding $ \mathbf{r}\times (\mathbf{a}+\mathbf{b})=0 $ i.e., r is parallel to $ \mathbf{a}+\mathbf{b} $
or $ \mathbf{r}=\lambda (\mathbf{i}+\mathbf{j}+2\mathbf{i}-\mathbf{k}) $
$ \mathbf{r}=\lambda (3\mathbf{i}+\mathbf{j}-\mathbf{k}) $ for $ \lambda =1\Rightarrow \mathbf{r}=(3\mathbf{i}+\mathbf{j}-\mathbf{k}) $ .
BETA
