# NCERT Class 11-Math՚s: Chapter – 12 Introduction to Three Dimensional Geometry Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## 12.2 Solved Examples

Question 1:

Locate the points (i)

(ii) in space.

(i) To locate the point in space, we move units from along the positive direction of x-axis. Let this point be . From the point A moves units parallel to direction of y-axis. Let this point be . From the point B moves units along positive direction of z-axis. Let this point be Fig. (12.3) .

(ii) From the origin, move 2 units along the negative direction of x-axis. Let this point be . From the point A move units parallel to negative direction of y-axis.

Let this point be . From B move 3 units parallel to positive direction of z - axis. This is our required point (Fig. 12.4.)

Question 2:

Sketch the plane (i) (ii) (iii)

(i) The equation of the plan represents the plane and equation of the plane represents the plane parallel to plane at a distance 1 unit above plane. Now, we draw a plane parallel to plane at a distance 1 unit above plane Fig. 12.5 (a) .

(ii) The equation of the plane represents the plane and the equation of the plane represents the plane parallel to plane at a distance 3 unit above plane (Fig. 12.5 (b) ) .

(iii) The equation of the plane represents the plane and z = 3 represents the plane parallel to plane at a distance 3 unit above plane (Fig. 12.5 (c) ) .

Question 3:

Let L, M, N be the feet of the perpendiculars drawn from a point on the and axes respectively. Find the coordinates of L, M and N.

Since L is the foot of perpendicular from P on the x-axis, its y and z coordinates are zero. The coordinates of L is . Similarly, the coordinates of M and N are and , respectively.

Question 4:

Let L, M, N be the feet of the perpendicular segments drawn from a point on the and planes, respectively. What are the coordinates of L, M and N?

Since L is the foot of perpendicular segment from P on the plane, z-coordinate is zero in the plane. Hence, coordinates of L is . Similarly, we can find the coordinates of and , Fig. 12.6.