The length of perpendicular drawn from the point ( 2 , 3 , 4 ) to line 4 - x 2 = y 6 = 1 - z 3 , is

Step-by-step solution

Let P be the foot of the perpendicular drawn from A ( 2 , 3 , 4 ) to the given line l . Then, x - 4 - 2 = y 6 = z - 1 - 3 Now, any point on the line l is given by x = 4 - 2 λ , y = 6 λ , z = 1 - 3 λ The coordinates of P are ( 4 - 2 λ , 6 λ , 1 - 3 λ ) The direction ratios of AP are ( 4 - 2 λ - 2 , 6 λ - 3 , 1 - 3 λ - 4 ) i.e. ( 2 - 2 λ , 6 λ - 3 , - 3 - 3 λ ) And the direction ratios of l are - 2 , 6 and - 3 . Given, A P ⊥ l ∴   - 2 ( 2 -