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The locus of the foot of the perpendicular drawn from the origin to a plane passing through a fixed point (a, b, c) is
- a)x2 + y2 + z2 - ax - by - cz = 0
- b)(x-a)2 + ( y - b)2 + (z - c)2 + 2a ( x - a) + 2b ( x - b) + 2c ( x - c) = 0
- c)
- d)none fo the above
Correct answer is option 'A'. Can you explain this answer?
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The locus of the foot of the perpendicular drawn from the origin to a ...
The equation of a plane passing through a fixed point (a, b, c) is given by
A ( x - a) + B ( y - b) + C ( z - c) = 0 ...(i)
Let (α,β,γ) be the foot of perpendicular from the origin on the plane given by (i).
Then the point (α,β,γ) lies on (i)
∴ A(α-α) + B(β-b) + C(γ-c) = 0 ...(ii)
Further the line joining (0,0,0) to (α,β,γ) is normal to the plane, therefore
A ( x - a) + B ( y - b) + C ( z - c) = 0 ...(i)
Let (α,β,γ) be the foot of perpendicular from the origin on the plane given by (i).
Then the point (α,β,γ) lies on (i)
∴ A(α-α) + B(β-b) + C(γ-c) = 0 ...(ii)
Further the line joining (0,0,0) to (α,β,γ) is normal to the plane, therefore
Most Upvoted Answer
The locus of the foot of the perpendicular drawn from the origin to a ...
The equation of a plane passing through a fixed point (a, b, c) is given by
A ( x - a) + B ( y - b) + C ( z - c) = 0 ...(i)
Let (α,β,γ) be the foot of perpendicular from the origin on the plane given by (i).
Then the point (α,β,γ) lies on (i)
∴ A(α-α) + B(β-b) + C(γ-c) = 0 ...(ii)
Further the line joining (0,0,0) to (α,β,γ) is normal to the plane, therefore
A ( x - a) + B ( y - b) + C ( z - c) = 0 ...(i)
Let (α,β,γ) be the foot of perpendicular from the origin on the plane given by (i).
Then the point (α,β,γ) lies on (i)
∴ A(α-α) + B(β-b) + C(γ-c) = 0 ...(ii)
Further the line joining (0,0,0) to (α,β,γ) is normal to the plane, therefore
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The locus of the foot of the perpendicular drawn from the origin to a plane passing through a fixed point (a, b, c) isa)x2 + y2 + z2- ax -by - cz = 0b)(x-a)2 + ( y - b)2 + (z - c)2 + 2a ( x - a) + 2b (x - b) + 2c ( x - c) = 0c)d)none fo the aboveCorrect answer is option 'A'. Can you explain this answer?
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