The distance of the point P (-2,4,-5) from the line x+3 3 = y-4 5 = z+8 6 is

Step-by-step solution

Since the point is (-2,4,-5) , a =-2, ~b =4, c =-5 Given equation of line is x+3 3 = y-4 5 = z+8 6 x₁=-3, y₁=4, z₁=-8 d.r.s of the line are 3,5,6 d.c.s are 3 70 , 5 70 , 6 70 Perpendicular distance of point from the line is aligned & array r [ ( a -x₁ )^2+ ( b -y₁ )^2+ ( c - z ₁ )^2 ] - [ ( a -x₁ ) l+ ( b -y₁ ) m + ( c - z ₁ ) n ]^2 array = & 1^2+0+3^2- [ 1(3) 70 + 0(5) 70 + 3(6) 70 ]^2 = & 1+9- ( 3 70 + 18 70 )^2 = & 37 10 units aligned