Chapter 11
Find the distance between the following pairs of points: (i) (2, 3, 5) and (4, 3, 1) (ii) (-3, 7, 2) and (2, 4, -1) (iii) (-1, 3, - 4) and (1, -3, 4) (iv) (2, -1, 3) and (-2, 1, 3).
Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear.
Verify the following: (i) (0, 7, -10), (1, 6, - 6) and (4, 9, - 6) are the vertices of an isosceles triangle. (ii) (0, 7, 10), (-1, 6, 6) and (- 4, 9, 6) are the vertices of a right angled triangle. (iii) (-1, 2, 1), (1, -2, 5), (4, -7, 8) and (2, -3, 4) are the vertices of a parallelogram.
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, -1).
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.