NCERT Class 11 Mathematics Solutions: Chapter 12 –Introduction to Three Dimensional Geometry Miscellaneous Exercise Part 1

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1. Three vertices of a parallelogram are . Find the coordinates of the fourth vertex.

Answer:

The three vertices of a parallelogram are given as .

Consider the coordinates of the fourth vertex be .

A Parallelogram ABCD

A parallelogram ABCD are given as A (3,–1,2),B (1,2,–4),and C (–1,1,2).

We know that the diagonals of a parallelogram bisect each other.

So, in parallelogram bisect each other.

So, the coordinates of the fourth vertex are .

2. Find the lengths of the medians of the triangle with vertices

Answer:

Consider be the medians of the given triangle .

A Triangle ABC

A triangle ABC, and AD, BE and CF be the medians of triangle.

Since is the median, is the mid-point of .

Coordinates of point

Since is the median, is the mid-point of

Coordinates of point

Since is the median, is the-point of .

Coordinates of point

Length of

So, the length of the medians of are .