# 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

## Short Answer Type

**Question 1**:

Locate the points (i)

(ii) in space.

**Answer**:

(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)

**Answer**:

(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.

**Answer**:

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?

**Answer**:

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.

**Question 5**:

Let L, M, N are the feet of the perpendiculars drawn from the point on the and planes, respectively. Find the distance of these points L, M, N from the point P, Fig. 12.7.

**Answer**:

L is the foot of perpendicular drawn from the point to the plane. Therefore, the coordinate of the point L is . The distance between the point and is . Similarly, we can find the lengths of the foot of perpendiculars on and plane which are 3 and 4 units, respectively.