Locus of a point P which such that PA = PB where A = (0,3,2) and B = (2,4,1) is

Engineering

Mathematics

Plane and Its Different Forms

Locus of a Point

Distance from a Plane

Question

Locus of a point P which such that PA = PB where A = (0,3,2) and B = (2,4,1) is

None of these

9x − 2y + 4z − 5 = 0

2x + y − z = 4

x − 2y + z + 1 = 0

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Let the co-ordinate of P be (x,y,z)

Given the points A(0,3.2) and B(2,4,1)

Given,

PA = PB

or,

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

or, −6y + 9 − 4z + 4 =−4x + 4 − 8y + 16 − 2z+1 [ Squaring and then eliminating the higher power of x,y,z]

or,4x + 2y − 2z = 8

or, 2x + y − z = 4

So locus of P is 2x + y − z = 4