Thank you for reporting, we will resolve it shortly
Q.
Let $a=i+j$ and $b=2 i-k$. The point of intersection of the lines $r \times a=b \times a$ and $r \times b=a \times b$ is
Vector Algebra
Solution:
$r \times a=b \times a $
$\Rightarrow (r-b) \times a=\vec{0}$
$\Rightarrow r-b$ is paralllel to $a$
$\therefore r-b=\lambda a$
i.e. $r=b+\lambda a\,\,\,(1)$
Similarly, $r \times b=a \times b$ can be written as
$r=a+\mu b \,\,\,(2)$
For point of intersection of the two lines (1) and (2),
we get $b+\lambda a=a+\mu b $
$\Rightarrow \lambda=\mu=1$
Hence, the required point of intersection is given by
$r=a+b=i+j+2 i-k=3 i+j-k$