If the line x-1 2 = y+1 3 = z-1 4 and x -3 1 = y - k 2 = z 1 intersect, then k is equal to

Step-by-step solution

Given, two lines L₁: x-1 2 = y+1 3 = z-1 4 and L₂: x-3 1 = y-k 2 = z-0 1 Let L₁: x-1 2 = y+1 3 = z-1 4 =p and L₂: x-3 1 = y-k 2 = z-0 1 =q Any point P on line L₁ is of type P(2 p+1,3 p-1 and 4 p+1) and any point Q on the line L₂ is of type Q(q+3,2 q+k and q) Since, L₁ and L₂ are intersecting each other, hence, both point P and Q should coincide at the point of intersection. Corresponding co-ordinates of P and Q should be same. 2 p+1=q+3,3 p-1=2 q+k and 4 p+1=q On solving, 2 p+1=q+3 and 4 p+1=q , we get p=- 3 2 and