If the lines x-1 2 = y+2 3 = z-1 4 and x-3 1 = y- k 2 = z 1 intersect, then k has the value

Step-by-step solution

The given equation of lines are x-1 2 = y+2 3 = z-1 4 and x-3 1 = y- k 2 = z 1 Since the lines intersect, aligned & | array ccc x₂-x₁ & y₂-y₁ & z ₂- z ₁ a ₁ & ~b ₁ & c ₁ a ₂ & ~b ₂ & c ₂ array |=0 & | array ccc 2 & k +2 & -1 2 & 3 & 4 1 & 2 & 1 array |=0 & 2(3-8)-( k +2)(2-4)-1(4-3)=0 & -10+2 k +4-1=0 & 2 k -7=0 & k = 7 2 aligned