# NCERT Class 11-Math՚S: Chapter – 12 Introduction to Three Dimensional Geometry Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Check Whether the Statements in Example from 29 to 37 Are True or False

Question 29:

The y-axis and z-axis, together determine a plane known as plane.

Answer: True

Question 30:

The point lies in the octant.

Answer:

False, the point lies in the octant,

Question 31:

The x-axis is the intersection of two planes plane and plane.

Answer: True

Question 32:

Three mutually perpendicular planes divide the space into octants.

Answer: True

Question 33:

The equation of the plane represent a plane parallel to the plane, having a intercept of 6 units.

Answer: True

Question 34:

The equation of the plane represent the plane.

Answer: True

Question 35:

The point on the x-axis with x-coordinate equal to is written as .

Answer: True

Question 36

represent a plane parallel to the plane.

Answer: True

Match each item given under the column to its correct answer given under column .

Question 37:

 Column Column (a) If the centroid of the triangle is origin and two of its vertices are and then the third vertex is (i) Parallelogram (b) If the mid-points of the sides of triangle are , and then the centriod is (ii) (c) The points , , and are the vertices of a (iii) (d) Point , and C are (iv) (e) Points , and are the vertices of (v) Collinear

Answer: (a)

Let , , be the vertices of a with centriod

Therefore, . This implies

Hence , , and . Therefore

(b) Let ABC be the given Δ and DEF be the mid-points of the sides , respectively. We know that the centriod of the centriod of .

Therefore, centriod of is

Hence

(C) Mid-point of diagonal is

Mid-point of diagonal BD is

Diagonals of parallelogram bisect each other. Therefore

(d)

Now . Hence Points A, B, C are collinear. Hence

(e)

Now . Hence ABC is an isosceles right angled triangle and hence