The distance of the point (1,2,-4) from the line x-3 2 = y-3 3 = z+5 6 is

Step-by-step solution

Given, point (1,2,-4) . aligned & and line x-3 2 = y-3 3 = z+5 6 = (let) & aligned & & x &=2 +3 & & x &=2 +3, y=3 +3, z=6 -5 aligned aligned Let P(2 +3,3 +3,6 -5) be the foot of perpendicular from A(1,2,4) Direction ratios of A P are 2 +3-1,3 +3-2,6 -5+4 i.e., 2 +2,3 +1,6 -1 And direction ratios of given line are 2,3,6 . Since, P given line array cc & 2(2 +2)+3(3 +1)+6(6 -1)=0 & 4 +4+9 +3+36 -6=0 array 49 +1=0 =- 1 49 P(2 +3,3 +3,6 -5) Distance of the point (1,2,-4) from the given line, aligned A P² &=(2 +2)²+(3 +1