If is the angle between the lines x-1 2 = 2y+3 4 ; z = -2 and x = 1; y-1 2 = z+1 2 , then

Step-by-step solution

The equation of the first line can be rewritten as x-1 2 = y+ 3 2 2 = z+2 0 The direction ratios of the first line are 2, 2, 0 . The equation of the second line can be rewritten as x-1 0 = y-1 2 = z+1 2 The direction ratios of the second line are 0, 2, 2 . Let be the angle between the two lines. = a₁a₂ + b₁b₂ + c₁c₂ a₁^2+b₁^2+c₁^2 a₂^2+b₂^2+c₂^2 = 2(0) + 2(2) + 0(2) 2^2+2^2+0^2 0^2+2^2+2^2 = 4 8 8 = 4 8 = 1 2 = 3 Answer: = 3