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:

Match Each Item Given under the Column
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