Coordinates of a Point in Space

Q.

Perpendicular distance of P(x, y, z ) from XY, YZ and XZ planes respectively are 1, 2 and 3. Which of the following could be the coordinates of P?

1. (-1, -2, -3)

2. (-1, 2 , -3)

3. (-2, 3, 1)

4. (2, -3, 1)

Q.

In the given figure of cuboid if the coordinates of point E is (3, 2 , 1) and one of the corners as the origin.

How many of the following coordinates are correct?

A(0, 1, 0) B(3, 0, 1) C(3, 0, 0) D(2, 3, 0)

E(3, 2, 1) F(0, 2, 0) G(0, 2, 1) H(0, 0, 0)

Q.

In the given figure of cuboid if the coordinates of point E is (3, 2 , 1) and one of the corners as the origin.

How many of the following coordinates are correct?

A(0, 1, 0) B(3, 0, 1) C(3, 0, 0) D(2, 3, 0)

E(3, 2, 1) F(0, 2, 0) G(0, 2, 1) H(0, 0, 0)

Q.

A line segment joining (1, 0, 1) and the origin (0, 0, 0) is revolved about the x-axis to form a right circular cone. If (x, y, z) is any point on the cone other than the origin, then it satisfies the equation

1. $x^2-2y^2-z^2=0$

2. $x^2-y^2-z^2=0$

3. $x^2-2y^2-2z^2=0$

4. $2x^2-y^2-2z^2=0$

Q. The coordinates of the point P are given by (2, -4, 5). Then,

1. Distance of point P from the XY plane = 5
2. Distance of point P from the XZ plane = $\sqrt{29}$
   
3. Distance of point P from the YZ plane = 2
   

4. Distance of point P from the XZ plane = 4

Q.

The coordinates of a point are (3, -2, -5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.

Q.

A cube of side 5 has one vertex at the point (1, 0, -1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive z-axis. Find the coordinates of the other vertices of the cube.

Q.

How many of these are correctly matched ?

Coordinates of a point Name of the octant

1. $(1,2,3)P.I$

2. $(4,-2,3)Q.IV$

3. $(4,-2,-5)R.VIII$

4. $(4,2,-5)S.V$

5. $(-4,2,-5)T.VI$

6. $(-4,2,5)U.II$

7. $(-3,-1,6)V.III$

8. $(2,-4,-7)W.VIII$

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Q.

Perpendicular distance of P(x, y, z ) from XY, YZ and XZ planes respectively are 1, 2 and 3. Which of the following could be the coordinates of P?

1. (-1, -2, -3)

2. (-1, 2 , -3)

3. (-2, 3, 1)

4. (2, -3, 1)

Q.

A cuboid is drawn in 3-D space. Length, width and height of the cuboid is 3, 2 and 1 unit respectively. X, Y and Z axes are given with one of the corners as the origin.

How many of the following coordinates are correct?

A (0, 1, 0)

B (3, 0, 1)

C (3, 0, 0)

D (2, 3, 0)

E (1, 2, 3)

F (0, 2, 0)

G (0, 2, 1)

H (0, 0, 0)

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