**NCERT Solutions for Maths Class
12 Exercise 11.1**

Hello Students. Welcome to **maths-formula.com**. In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 11.1**.

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Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

**NCERT Solutions for Maths Class 12 Exercise 11.1** helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from **NCERT Syllabus for Mathematics Class 12**.

**NCERT Solutions for Maths Class 12 Exercise 11.1** are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

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**NCERT Solutions for Maths Class 12 Exercise 11.2**

**NCERT Solutions for Maths Class 12 Exercise 11.3**

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**NCERT Solutions for Maths Class 12 Exercise 11.1**

**Maths Class
12 Ex 11.1 Question 1.**

If a line makes
angles 90°, 135°, 45° with the x, y and z-axes respectively, find its direction
cosines.

**Solution:**

If a line makes
angles 90°, 135°, 45° with the x, y and z-axes, then the direction cosines are:
l = cos Î±, m = cos Î² and n = cos Î³. Here, Î± = 90°, Î² = 135°, Î³ = 45°

**Maths Class
12 Ex 11.1 Question 2.**

Find the
direction cosines of a line which makes equal angles with the coordinate axes.

**Solution:**

If a line makes
angles 90°, 135°, 45° with the x, y and z-axes, then the direction cosines are:
l = cos Î±, m = cos Î² and n = cos Î³. Here, Î± = Î² = Î³.

Thus l = m = n =
cos Î±

But, l² + m² + n² = 1

∴
cos² Î± + cos² Î± +
cos² Î± = 1

**Maths Class
12 Ex 11.1 Question 3.**

If a line has the
direction ratios –18, 12, –4, then what are its direction cosines?

**Solution:**

The given
direction ratios of a line are –18, 12 and –4.

∴ a = –18, b = 12 and c = –4

Thus, the direction cosines of the line are:

**Maths Class
12 Ex 11.1 Question 4.**

Show that the
points (2, 3, 4), (–1, –2, 1), (5, 8, 7) are collinear.

**Solution:**

Let the points be
A(2, 3, 4), B(–1, –2, 1) and C(5, 8, 7).

Then the direction ratios of AB be

**Maths Class
12 Ex 11.1 Question 5.**

Find the
direction cosines of the sides of the triangle whose vertices are (3, 5, –4), (–1,
1, 2) and (–5, –5, –2).

**Solution:**

The vertices of
triangle ABC are A(3, 5, –4), B(–1, 1, 2) and C(–5, –5, –2).