The length of the perpendicular from the point (0,2,3) on the line x+3 5 = y-1 2 = z+4 3

Step-by-step solution

Any point on the line x+3 5 = y-1 2 = z+4 3 = can be taken as (5 -3,2 +1,3 -4) aligned & for foot of perpendicular = a ( -x₁ )+b ( -y₁ )+c ( -z₁ ) a^2+b^2+c^2 & = 5(0+3)+2(2-1)+3(3+4) 5^2+2^2+3^2 & i.e., =1 & foot of perpendicular (2,3,-1) & Length of the perpendicular = (0-2)^2+(2-3)^2+(3+1)^2 & = 21 aligned