Chapter 12: Introduction to Three Dimensional Geometry

Q1. Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).

Ans: x – 2z = 0.

Q2. Given that P (3, 2, –4), Q (5, 4, –6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR.

Ans: 1:2

Q3. Prove that the points: (0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of a right-angled triangle

Q4. Choose the correct answer:

Calculate the perpendicular distance of the point P(6, 7, 8) from the XY – Plane.

(a)8  (b)7   (c)6  (d) None of the above

Q5. Find the distance between the points P(-2,4,1) and Q(1, 2, – 5).

Ans: 7 units

Q6. Choose the correct answer:

The point (-2, -3, -4) lies in the
(a) First octant
(b) Seventh octant
(c) Second octant
(d) Eighth octant

Q7. Find the image of (-2,3,4) in the y z plane

Ans. (2, 3, 4)

8. Find the distance from the origin to (6, 6, 7).

Ans: 11

9. Show that the points A(0,1,2) B(2,-1,3) and C(1,-3,1) are vertices of an isosceles right angled triangle.

10. Three vertices of a parallelogram ABCD are A(3,−1,2),B(1,2,−4) and C(−1,1,2). Find the coordinates of the fourth vertex.

Ans: (1,−2,8)