NIOS maths 311 book 2 Three dimensional Geometry 33.2 solutions ( maths class 12)

NIOS Mathematics 311 book 2 Module IX Chapter Three-Dimensional Geometry Check your progress 33.2 solutions are given.

You should study the textbook lesson Three-Dimensional Geometry very well.

You should also observe and practice all example problems and solutions given in the textbook.

You can observe the solutions given below and try them in your own method.

Three Dimensional Geometry

Three Dimensional Geometry 33.2 Solutions NIOS class 12 ( maths class 12)

Maths class 12 NIOS

Three Dimensional Geometry

Chapter 33

Check your progress 33.2

1. Find the distance between the following points: a. (4, 3, -6)

b. (-3, 1, -2) and (-3, -1, 2)

c. (0, 0, 0) and (-1, 1, 1)

2. Show that if distance between the points (5, -1, 7) and (a, 5, 1) is 9 units. “a” must be either 2 or 8.

3. Show that the triangle formed by the points (a, b, c), (b, c, a) and (c, a, b) is equilateral.

4. Show that the points (-1, 0, -4) and (0, 1, -6) and (1, 2, -5) from a right-angled triangle.

5. Show that the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of an isosceles right-angled triangle.

6. Show that the points (3, -1, 2), (5, -2, -3), (-2, 4, 1) and (-4, 5, 6) form a parallelogram.

7. Show that the points (2, 2, 2), (-4, 8, 2), (-2, 10, 10) and (4, 4, 10) form a square.

8. Show that in each of the following cases the three points are collinear.

a. (-3, 2, 4), -(1, 5, 9) and (1, 8, 14)

b. (5, 4, 2), (6, 2, -1) and (8, -2, -7)

c. (2, 5, -4), (1, 4, -3) and (4, 7, -6)

Note ; Observe the solutions and try them in your own method.