**NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three
Dimensional Geometry Ex 12.2**

NCERT Solutions for Class
11 Maths Chapter 12
Introduction to Three Dimensional Geometry Ex 12.2 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 12.2.

**Ex 12.2 Class 11 Maths Question 1.**

**Find the distance between the following pairs of points:**

**(i)**(2, 3, 5) and (4, 3, 1)

**(ii)**(-3, 7, 2) and (2, 4, -1)

**(iii)**(-1, 3, -4) and (1, -3, 4)

**(iv)**(2, -1, 3) and (-2, 1, 3)

**Solution:**

**Ex
12.2 Class 11 Maths Question 2:**

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

**Solution:**

**the points P(-2, 3, 5), Q(1, 2, 3) and R(7, 0, -1) are collinear.**

**Ex 12.2 Class 11
Maths Question 3:**

**Verify the following:**

**(i)** (0, 7,
-10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles
triangle.

**(ii)** (0, 7, 10), (-1, 6, 6) and (-4, 9, 6)
are the vertices of a right-angled triangle.

**(iii)** (-1, 2, 1), (1, -2, 5), (4, -7, 8) and
(2, -3, 4) are the vertices of a parallelogram.

**Solution:**

Therefore, ABCD is a
parallelogram.

Hence, the given points are
the vertices of a parallelogram.

**Ex 12.2 Class 11
Maths Question 4:**

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

**Solution:**

Let P(x, y, z) be the point that is equidistant from the points A(1, 2,
3) and B(3, 2, -1).

Therefore, PA = PB

Or, PA^{2} = PB^{2}

(x – 1)^{2} + (y – 2)^{2} + (z – 3)^{2} = (x –
3)^{2} + (y – 2)^{2} + (z + 1)^{2}

x^{2} – 2x + 1 + y^{2} – 4y + 4 + z^{2} – 6z + 9
= x^{2} – 6x + 9 + y^{2} – 4y + 4 + z^{2} + 2z + 1

-2x – 4y – 6z + 14 = -6x – 4y + 2z + 14

4x – 8z = 0

x – 2z = 0

Thus, the required equation is x – 2z = 0.

**Ex 12.2 Class 11
Maths Question 5:**

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

**Solution:**

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