NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter : INTRODUCTION TO THREE DIMENSIONAL GEOMETRY
Long Answer Questions

Question. 18

Show that the three points A (2, 3, 4), B (−1, 2, −3) and C (−4, 1, −10) are collinear and find the ratio in which C divides AB.

Answer:

2:1 externally

Question. 19

The mid-point of the sides of a triangle are (1, 5, −1), (0, 4, −2) and (2, 3, 4). Find its vertices. Also find the centroid of the triangle.

Answer:

vertices are (3,4,5), (−1,6,−7), (1,2,3) and centroid is (1,4, 1/3)

Question. 20

Prove that the points (0, −1, −7), (2, 1, −9) and (6, 5, −13) are collinear. Find the ratio in which the first point divides the join of the other two.

Answer:

1:3 externally

Question. 21

What are the coordinates of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and the three edges passing through the origin coincide with the positive direction of the axes through the origin?

Answer:

(2,0,0), (2,2,0), (0,2,0), (0,2,2), (2,0,2), (0,0,0), (2,2,2)

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