Question

Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane 5y + 8 = 0
1. \(\left( {0, - \frac{8}{5},0} \right)\)
2. \(\left( {\frac{8}{{25}},0,0} \right)\)
3. \(\left( {0, \frac{8}{5},0} \right)\)
4. \(​​\left( {0, - \frac{{18}}{5},2} \right)\)

Answer 1

Correct Answer - Option 1 : \(\left( {0, - \frac{8}{5},0} \right)\)

Calculation:

The equation of the plane is 5y + 8 = 0, i.e.,

0x + 5y + 0z = -8

The direction ratio are (0, 5, 0)

Let the co-ordinates of the foot of the perpendicular be (x, y, z)

So equation of the perpendicular line will be 

\(\rm {x-0\over 0}= {y-0\over 5}= {z-0\over 0}\) = r (say)

x = 0, y = 5r and z = 0

As the point satisfy the equation of the plane, 

∴ 5y + 8 = 0

5(5r) + 8 = 0

r = \(-8\over25\)

So y = 5r = \(-8\over5\)

∴ The coordinates are (0, \(-8\over5\), 0)