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Chapter 28: Introduction to 3D coordinate geometry – Exercise 28.1

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.1(i)

Ans.

All are positive. So octant is XOYZ

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.1(ii)

Ans.

X is negative and rest are positive, so octant is X’OYZ

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.1(iii)

Ans.

Y is negative and rest are positive, so octant is XOY’Z 

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.1(iv)

Ans.

Z is negative and rest are positive, so octant is XOYZ’

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.1(v)

Ans.

X and Y are negative and Z is positive, so octant is X'OY'Z

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.1(vi)

Ans.

All are negative, so octant is X’OY’Z’

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.1(vii)

Ans.

Y and Z are negative, so octant is XOY’Z’

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.1(viii)

Ans.

X and Z are negative, so octant is X’OYZ’

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.2(i)

Ans.

YZ plane is x-axis, so sign of x will be changed. So answer is (2, 3, 4)

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.2(ii)

Ans.

XZ plane is y-axis, so sign of y will be changed. So answer is (-5, -4, -3)

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.2(iii)

Ans.


XY-plane is z-axis, so sign of Z will change. SO answer is (5, 2, 7)

 



Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.2(iv)

Ans.


XZ plane is y-axis, so sign of Y will change, So answer is (-5. 0. 3)

 



Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.2(v)

Ans.


XY plane is Z-axis, so sign of Z will change So Answer is (-4, 0, 0)

 



Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.3

Ans.


Vertices of cube are

(1, 0, -1) (1, 0, 4) (1, -5, -1)

(1, -5, 4)(-4, 0, -1)(-4, -5, -4)

(-4, -5, -1) (4, 0, 4)(1, 0, 4)

 





Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.4

Ans.


3 – (-2) = 5, |0, -5| = =5,| – 1 – 4| = 5

5, 5, 5 are lengths of edges

 



Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.5

Ans.


5 – 3 = 2, 0 – (- 2) = 2, 5 – 2 = 3

2, 2, 3 are lengths of edges.

 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.6

Ans.



 

Introduction to 3D coordinate geometry – Exercise – 28.1 – Q.7

Ans.

(-3, -2, -5) (-3, -2, 5) (3, -2. -5) (-3, 2, -5) (3, 2, 5) (3, 2, -5) (-3, 2, 5)

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