Find the co-ordinates of the foot of the perpendicular drawn from the

1.	Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane 5y + 8 = 01. \(\left( {0, - \frac{8}{5},0} \right)\)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» 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)

Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane 5y + 8 = 01. \(\left( {0, - \frac{8}{5},0} \right)\)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» 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)

Discussion

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