The length of perpendicular drawn from the point (3,-1,11) to the line x 2 = y-2 3 = z-3 4 is

Step-by-step solution

Let the foot point of the perpendicular drawn from the point P(3,-1,1) on the straight line be L . Hence, L lies on the straight line L(2 t, 2+3 t, 3+4 t) [where, t is arbitrary constant] The direction ratios of P L are (2 t-3,2+3 t+1 , Again, the direction ratios of the straight line. x 2 = y-2 3 = z-3 4 are (2,3,4) . Since, P L is perpendicular on the straight line. Then, (2 t-3) 2+(3 t+3) 3+(4 t-8) 4=0 aligned & 4 t-6+9 t+9+16 t-32=0 & 29 t=29 aligned t=1 Hence, L(2,5,7) (P L)= (2-3)^2+(5+1)^2+(7-11)^2 = 53