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Q.

Let A(0, 6, 8) and B(6, 12, 0) be two given points and  Pa,0,0  be a point on x–axis such that PA+PB is minimum, then which of the following is/are true?

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a

Perpendicular distance from the point A to the plane containing the points P, Q, B is 8 units

b

If point Q is on the yaxis such that QA+QB is minimum then area of  ΔPOQ  is 907  unit2 where O is origin

c

The volume of tetrahedron OPAB (where O is origin) is 24011 unit3

d

The volume of tetrahedron OPAB (where O is origin) is 48011 unit3

 

answer is A, C, D.

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Detailed Solution

α=3011,Q0,667,0

 

Question Image

 

 

PA+PB is minimum, then       So, MPPN=AMBN=56

So, P=3011,0,0  Similarly Q is 0,667,0

 

 

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