Vector Algebra Question 159
Question: If $ a=i+j $ and $ b=2i-k $ are two vectors, then the point of intersection of two lines $ r\times a=b\times a $ and $ r\times b=a\times b $ is
[RPET 2000]
Options:
A) i + j ? k
B) i ? j + k
C) 3i + j ? k
D) 3i ? j + k
Show Answer
Answer:
Correct Answer: C
Solution:
- Let $ \mathbf{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k} $ , then $ \mathbf{r}\times \mathbf{a}=\mathbf{b}\times \mathbf{a} $
Þ $ (\mathbf{r}-\mathbf{b})\times \mathbf{a}=0 $
$ \Rightarrow | \begin{aligned} & ijk \\ & x-2yz+1 \\ & 1,10 \\ \end{aligned} |=0 $ ,
$ \therefore z=-1,x-y=2 $ Now $ \mathbf{r}\times \mathbf{b}=\mathbf{a}\times \mathbf{b} $
Þ $ (\mathbf{r}-\mathbf{a})\times \mathbf{b}=0 $
$ \therefore y=1,x+2z=1 $
$ \Rightarrow x=3,y=1,z=-1 $ \ $ \mathbf{r}=3\mathbf{i}+\mathbf{j}-\mathbf{k} $ .
BETA
