Hello Students. In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 11.1**.

You can download the **PDF of NCERT Books Maths Chapter 10** for your easy reference while studying **NCERT Solutions for Maths Class 12 Exercise 11.1**.

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**.

If you want to recall **All Maths Formulas for Class 12**, you can find it by clicking this link.

If you want to recall **All** **Maths Formulas for Class 11**, you can find it by clicking this link.

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

** **

**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).

**Related Link:**