If the lines x−12=y+13=z−14 and x−31=y−k2=z1 intersect, then the value of k is -
92
Since the lines intersect, therefore they must have a point in common, i.e.
x−12=y+13=z−14=λandx−31=y−k2=z1=μ⇒x=2λ+1,y=3λ−1z=4λ+1
and x=μ+3,y=2μ+k,z=μ are same.
⇒2λ+1=μ+33λ−1=2μ+k4λ+1=μ
On solving these equations, we get,
λ=−32 and μ=−5∴k=3λ−2μ−1⇒k=3(−32)−2(−5)−1=92∴k=92