Find a point in XY plane which is equidistant from three points (2, 0, 3), (0, 3, 2) and (0, 0, 1).

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(a)

Find the locus of the point which is equidistant from A(3, 4, 0) and B(5, 2, -3).

5

(a)

Given that P(5, 4, -2), Q (7, 6, -4) and R (11, 10, -8) are collinear points. Find the ratio in which Q divides PR.

5

(a)

Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex.

5

(a)

Show that the coordinates of the centroid of a triangle with vertices A(x₁,x ₂,x₃)., b(y₁,y ₂,y ₃), c(z₁,z₂,z ₃) are \(\left[ \frac { x1+x2+x3 }{ 3 } ,\frac { y1+y2+y3 }{ 3 } ,\frac { z1+z2+z3 }{ 3 } \right] \)

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(a)

Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0) and (6, 0, 0).

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(a)

A point R with x-coordinate 4 lies on the line segment joining the points P(2,-3, 4) and Q(8, 0,10). Find the coordinates of the point R.
Suppose R divides PQ in the ratio k : 1. The coordinates of the point R all given by \(\left( \frac { 8k+2 }{ k+1 } ,\frac { -3 }{ k+1 } ,\frac { 10k+4 }{ k+1 } \right) \).

5

(a)

If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R(8, 14, 2c), then find the values of a, b and c.

5

(a)

Find the coordinates of a point on y-axis which are at a distance of \(5\sqrt { 2 } \)  from the point P(3, -2,5).

5

(a)

If A and B be the points (3, 4, 5) and (–1, 3, –7), respectively, find the equation of the set of points P such that PA²+PB²=K² where k is a constant.

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(a)