Question

# Find the distance of the point (-2,3,-4) from the line x+2/3 = 2y+3/4=3z+4/5 measure parallel to the plane 4x+12y-3z+1=0.

Solution

## Equation of given line is (x+2)/3=(2y+3)/4=(3z+4)/5=λ (say) Therefore Any point on this line is of the form, [3λ-2,(4λ-3)/2, (5λ-4)/3] Now, D.R.S of the line from the point (-2,3,-4) is 3λ,(4λ-9)/2,(5λ+8)/3 Also the Equation of Plane is given as 4x+12y-3z+1=0 Therefore D.R.S of Normal= 4,12,-3 Now the normal of plane is perpendicular to the drs of above line . Hence, 4.3λ+12[(4λ-9)/2]-3[(5λ+8)/3]=0 => 12λ+24λ-54-5λ-8=0 => 31λ=62 =>λ=2 Hence the required Coordinate is (4,5/2,2) Hence Distance Between Coordinates (4,5/2,2) and (-2,3,-4) is 17/2 units( By Distance Formula)

Suggest corrections