NCERT Class 11-Math's: Chapter –12 Introduction to Three Dimensional Geometry Part 5

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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

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