# NCERT Class 11-Math՚s: Chapter – 12 Introduction to Three Dimensional Geometry Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 19**:

What is the perpendicular distance of the point from plane?

(A)

(B)

(C)

(D) None of these

**Answer**:

Let L be the foot of perpendicular drawn from the point to the plane and the distance of this foot L from P is *z*-coordinate of , i.e.. , units.

**Question 20**:

L is the foot of the perpendicular drawn from a point on the plane. What are the coordinates of point L?

(A)

(B)

(C)

(D) None of these

**Answer**:

Since L is the foot of perpendicular from P on the plane, *z*-coordinate is zero in the plane. Hence, coordinates of L are .

**Question 21**:

L is the foot of the perpendicular drawn from a point on *x-*axis. The coordinates of L are

(A

(B)

(C)

(D) None of these

**Answer**:

Since L is the foot of perpendicular from P on the *x*- axis, *y* and *z*-coordinates are zero. Hence, the coordinates of L are .

**Question 22**:

What is the locus of a point for which ?

(A) Equation of *x*-axis

(B) Equation of *y-*axis

(C) Equation of *z*-axis

(D) None of these

**Answer**:

Locus of the point is *x*-axis, since on *x*-axis both and .

**Question 23**:

L, is the foot of the perpendicular drawn from a point on the plane. What are the coordinates of point L?

(A)

(B)

(C)

(D)

**Answer**:

Since L is the foot of perpendicular segment drawn from the point on the plane. Since the *y*-coordinates of all points in the plane are zero, coordinate of the foot of perpendicular are .

## Fill in the Blanks in Examples 24 to 28

**Question 24**:

A line is parallel to plane if all the points on the line have equal ________.

**Answer**:

A line parallel to plane if all the points on the line have equal *z*-coordinates.

**Question 25**:

The equation represents a plane parallel to ________ plane.

**Answer**:

Since represent plane, therefore represent a plane parallel to plane at a unit distance from the origin.

**Question 26**:

Perpendicular distance of the point from axis is ________

**Answer**:

Since M is the foot of perpendicular from P on the *y*-axis, therefore, its *x* and coordinates are zero. The coordinates of M is . Therefore, the perpendicular distance of the point P from axis

**Question 27**:

L is the foot of perpendicular drawn from the point on planes. The coordinates of L are ________.

**Answer**:

Since L is the foot of perpendicular from P on the plane, coordinate of every point is zero in the plane. Hence, coordinate of L are .

**Question 28**:

The length of the foot of perpendicular drawn from the point on *z*-axis is ________.

**Answer**:

The coordinates of the foot of perpendicular from the point on *z* axis is . The distance between the point and is