NCERT Class 11 Mathematics Solutions: Chapter 12 –Introduction to Three Dimensional Geometry Miscellaneous Exercise Part 2

1. If the origin is the centroid of the triangle with vertices , then find the values of

Answer:

The Triangle PQR

The triangle PQR with vertices P(2a,2,6), Q(-4,3b,-10) and R( 8, 14,2c).

It is known that the coordinates of the centroid of the triangle, whose vertices are and , are

So, coordinates of the centroid of

It is given that origin is the centroid of .

So, the respective values of are .

2. Find the coordinates of a point on y-axis which are at a distance of from the point .

Answer:

If a point is on the y-axis, then x-coordinate and the z-coordinate of the point are zero.

Consider be the point on the y-axis at a distance of from point .

Accordingly,

So, the coordinates of the required points are .