Question

Find The equation of the perpendicular drawn from the point P(2,4,-1) to the line
x+5/1=y+3/4=z-6/-9.Also write down the coordinates of the foot of the perpendicuar from P to the line

Answer 1

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Direction Ratios of PQ are λ - 7, 4λ -7, -9λ + 7

Since PQ ⊥ AB then a₁a₂ + b₁b₂ + c₁c₂ = 0

or (λ - 7) 1 + (4λ - 7) 4 + (-9λ + 7) (-9) = 0

or 98λ = 98 or λ = 1

d.r.'s of PQ are -6,-3 -2 or 6,3,2

Equation of PQ is x-2/6 = y - 4/3 = z + 1/2

By putting λ = 1

Co-ordinates of foot of ⊥ (-4,1,-3)

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