# 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