NCERT Solutions Class 11 Mathematics Chapter 12 Download In Pdf

Chapter 12 Introduction To Three Dimensional Geometry Download in pdf

**Question 1.** A point is on the x-axis. What are its y-coordinate and z-coordinates?

**Question 2.**A point is in the XZ-plane. What can you say about its y-coordinate?

**Question 3.**Name the octants in which the following points lie:

(1,. 2, 3), (4, β2, 3), (4, β2, β5), (4, 2, β5), (β 4, 2, β5), (β 4, 2, 5),
(β3, β1, 6) (2, β 4, β7).

**Question 4.**Fill in the blanks:

(i) The x-axis and y-axis taken together determine a plane known as_______.

(ii) The coordinates of points in the XY-plane are of the form _______.

(iii) Coordinate planes divide the space into ______ octants.

EXERCISE 12.2

**Question 1.** Find the distance between the following pairs of points:

(i) (2, 3, 5) and (4, 3, 1) (ii) (β3, 7, 2) and (2, 4, β1)

(iii) (β1, 3, β 4) and (1, β3, 4) (iv) (2, β1, 3) and (β2, 1, 3).

**Question 2.**Show that the points (β2, 3, 5), (1, 2, 3) and (7, 0, β1) are collinear.

**Question 3.**Verify the following:

(i) (0, 7, β10), (1, 6, β 6) and (4, 9, β 6) are the vertices of an isosceles triangle.

(ii) (0, 7, 10), (β1, 6, 6) and (β 4, 9, 6) are the vertices of a right angled triangle.

(iii) (β1, 2, 1), (1, β2, 5), (4, β7, 8) and (2, β3, 4) are the vertices of a parallelogram

**Question 4.**Find the equation of the set of points which are equidistant from the points
(1, 2, 3) and (3, 2, β1).

**Question 5.**Find the equation of the set of points P, the sum of whose distances from
A (4, 0, 0) and B (β 4, 0, 0) is equal to 10.

EXERCISE 12.3

**Question 1.** Find the coordinates of the point which divides the line segment joining the points
(β 2, 3, 5) and (1, β 4, 6) in the ratio
(i) 2 : 3 internally, (ii) 2 : 3 externally.

**Question 2.**Given that P (3, 2, β 4), Q (5, 4, β 6) and R (9, 8, β10) are collinear. Find the ratio
in which Q divides PR.

**Question 3.**Find the ratio in which the YZ-plane divides the line segment formed by joining
the points (β2, 4, 7) and (3, β5, 8).

**Question 4.**Using section formula, show that the points A (2, β3, 4), B (β1, 2, 1) and
C 0 1 2
3 are collinear.

**Question 5.**Find the coordinates of the points which trisect the line segment joining the points
P (4, 2, β 6) and Q (10, β16, 6).

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

**Question 2.**Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0)
and (6, 0, 0).

**Question 3.**If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6),
Q (β 4, 3b, β10) and R(8, 14, 2c), then find the values of a, b and c.

**Question 4.**Find the coordinates of a point on y-axis which are at a distance of 5 2 from
the point P (3, β2, 5).

**Question 5.**A point R with x-coordinate 4 lies on the line segment joining the points
P(2, β3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint Suppose R divides PQ in the ratio k :1.The coordinates of the point R are given
by
, 10 4
1
, 3
1
8 2
k
k
k k
k ].
.

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- Chapter 1 Sets
- chapter 2 Relations And Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations And Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences And Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction To Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability

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