Find the ratio in which the straight line joining the points (2,-3,5) and (7,1,3) is divided by the xy plane.
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A(2,-3,5) B(7,1,3)
Line AB meets x-y plane at P(x,y, 0). Both points A & B are on one side of the x-y plane as z coordinates are both positive.
AP : BP = (z coordinate of A - z coordinate of P) / (z coordinate of B - z coordinate of P)
= (5 - 0) / (3 - 0) = 5 : 3
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we can also find the coordinates of P and then find AP, BP too.
equation of AB : x = 2 + 5 t
y = -3 + 4 t
z = 5 - 2 t
z is 0 for t = 2.5. Hence
P = (14.5, 7, 0).
So AP = √(12.5²+10²+5²) = 15√5 /2
BP = √(7.5²+ 6² + 3²) = 9√5 /2
AP : BP = 5 : 3
Line AB meets x-y plane at P(x,y, 0). Both points A & B are on one side of the x-y plane as z coordinates are both positive.
AP : BP = (z coordinate of A - z coordinate of P) / (z coordinate of B - z coordinate of P)
= (5 - 0) / (3 - 0) = 5 : 3
=====
we can also find the coordinates of P and then find AP, BP too.
equation of AB : x = 2 + 5 t
y = -3 + 4 t
z = 5 - 2 t
z is 0 for t = 2.5. Hence
P = (14.5, 7, 0).
So AP = √(12.5²+10²+5²) = 15√5 /2
BP = √(7.5²+ 6² + 3²) = 9√5 /2
AP : BP = 5 : 3
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