**NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three
Dimensional Geometry Ex 12.3**

NCERT Solutions for Class
11 Maths Chapter 12
Introduction to Three Dimensional Geometry Ex 12.3 are the part of NCERT
Solutions for Class 11 Maths. Here you can find the NCERT Solutions for Class
11 Maths Chapter 12 Introduction to Three Dimensional Geometry Ex 12.3.

**Ex 12.3 Class 11 Maths Question 1.**

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

**(ii)**2 : 3 externally

**Solution:**

**(i)** Let P(x, y, z) be any point which divides the line segment
joining the points A(-2, 3, 5) and B(1, -4, 6) in the ratio 2 : 3 internally.

**(ii)** Let P(x, y, z) be any point which
divides the line segment joining the points A(-2, 3, 5) and B(1, -4, 6) in the
ratio 2 : 3 externally. Then

**Ex 12.3 Class 11 Maths
Question 2.**

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.

**Solution:**

Let Q(5, 4, -6) divides the line segment joining the points P(3, 2, -4) and
R(9, 8, -10) in the ratio k : 1 internally.

**Ex 12.3 Class 11 Maths Question 3.**

Find the ratio
in which the YZ-plane divides the line segment formed by joining the points
(-2, 4, 7) and (3, -5, 8).

**Solution:**

Let the
ratio in which the YZ-plane divides the line segment formed by joining the
points A(-2, 4, 7) and B(3, -5, 8) at a point C be k : 1.

**Ex 12.3 Class 11 Maths Question 4.**

Using section formula, show that the points A(2, -3, 4), B(-1, 2, 1) and C(0, 1/3, 2) are collinear.

**Solution:**

Let the points A(2, -3, 4), B(-1, 2, 1) and C(0, 1/3, 2) be the given points. Let the point P divides
AB in the ratio k : 1. Then, the coordinates of P are [(−k+2)/(k+1), (2k−3)/(k+1), (k+4)/(k+1)]

Let us examine whether for some value of k, the point P coincides with point C.

**Ex 12.3 Class 11 Maths
Question 5.**

Find the coordinates of the points which trisect the line segment joining the
points P(4, 2, -6) and Q(10, -16, 6).

**Solution:**

Let R and S be two points which trisect the line segment joining the points
P(4, 2, -6) and Q(10, -16, 6).

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