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Q1. Write the coordinates of points in the Y-Z plane

Solution

The coordinates of points in the Y-Z plane are (0,y,z).

Q2. A point is in the YZ plane. What is the value of the x-coordinate?

Solution

Since the point lies in the YZ plane the value of x-cordinate is zero.

Q3. Find the locus of P if PA² + PB² = 2k² where A and B are the points (3,4,5) and (-1,3,-7).

Solution

Let P(x,y,z) be the point whose locus is to be found, NowPA² + PB² = 2k².(x - 3)² + (y - 4)² + (z - 5)² + (x + 1)² + (y - 3)² + (z + 7)² =2k²x² - 6x + 9 + y² - 8y + 16 + z² - 10z + 25 + x² + 2x + 1 + y² - 6y + 9 + z² + 14z + 49 = 2k²2x² + 2y² + 2z² - 4x - 14y + 4z + 109 = 2k².

Q4. A point P is on the x-axis. What are its y-coordinate and z-coordinate?

Solution

The point lies on the x-axis hence the y and z co-ordinates are zero. The co-ordinates of P are (x,0,0).

Q5. Write the coordinates of points in the X-Y plane.

Solution

The coordinates of points in the XY- plane are (x,y,0).

Q6. A points P is on the y-axis. What are its x-coordinate and z-coordinates?

Solution

The point lie on the y-axis, hence the x and z-coordinates are zero. The coordinate of P are (o,y,o).

Q7. Name the octant in which the following points lie : (i) (4,-2,-5) (ii) (-4,2,-5)(iii) (1,2,3)

Solution

(i) VIIIth Octant (ii) VIth Octant (iii) Ist Octant

Q8. A point P is at a distance of 6 units from the origin on the Z axis. Write the coordinates of P

Solution

The coordinates of P are 

Q9. A point is in the XZ-plane. What is the value of the y-coordinate.

Solution

Since the point lie in the XZ plane the value of y coordinate is zero.

Q10. A point P is at a distance of 3 units from the origin on the y axis. Write the coordinates of P.

Solution

The coordinates of P are .

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