# CBSE Class 11-science Maths Distance Formula:3 D Geometry

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- Find the distance between the points P and Q having coordinates (2,3,1) and (-2,4,-1).
- Using distance formula prove that the points A(4,-3,-1), B(5,-7,6) and C(3,1,-8) are collinear.
- Determine the point in XY - plane which is equidistant from three points A(2,0,3) B(0,3,2) and C(0,0,1).
- Verify that the given points are the vertices of an isosceles triangle, A(0,7,-10), B(1,6,-6) and C(4,9,-,6).
- Prove that the points A(1,3,0), B(-5,5,2) C(-9,-1,2) and D(-3,-3,0) are the vertices of a parallelogram. Also show that ABCD is not a rectangle.
- If A (-2,2,3) and B(13,-3,13) are two points such that 3PA = 2PB, find the locus of P.
- Find the locus of P if PA
^{2}+ PB^{2}= 2k^{2}where A and B are the points (3,4,5) and (-1,3,-7). - Show that A(a,b,c), B(b,c,a) and C(c,a,b) are the vertices of an equilateral triagle.
- Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (-4, 0, 0) is equal to 10?

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