Show that line →r=(^i+^j−^k)+λ(3^i−^j) and →r=(4^i−^k)+μ(2^i+3^k) intersect. Also find their point of intersection.

x=y=z+10=λ− (1)
x=y=z+13=μ− (2)
Point on first line,[3λ+1,−λ+1,−1]− (3)
Point on second line,[2μ+4,0,3μ−1]− (4)
For point of intersection, equation3=equation4.
We get,λ=1,μ=0
Therefore, point of intersection is(4,0,−1).