Locus of a point P which such that P A = P B where A = \left(\right. 0 , 3 , 2 \left.\right) and B = \left(\right. 2 , 4 , 1 \left.\right) is

Engineering

Mathematics

Line of Greatest Slope

Question

Locus of a point

P

which such that

P A = P B

where

A = (0, 3, 2)

and

B = (2, 4, 1)

2 x + y - z = 4

x - 2 y + z + 1 = 0

9 x - 2 y + 4 z - 5 = 0

None of these

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Let the co-ordinate of

P

(x, y, z)

Given the points

A (0, 3.2)

and

B (2, 4, 1)

Given,

P A = P B

or,

\sqrt{x^{2} + (y - 3)^{2} + (z - 2)^{2}} = \sqrt{(x - 2)^{2} + (y - 4)^{2} + (z - 1)^{2}}

or,

- 6 y + 9 - 4 z + 4 = - 4 x + 4 - 8 y + 16 - 2 z + 1

[ Squaring and then eliminating the higher power of

x, y, z

]

or,

4 x + 2 y - 2 z = 8

or,

2 x + y - z = 4

So locus of

P

2 x + y - z = 4

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