NCERT Solutions for Maths Class 12 Exercise 11.1

# NCERT Solutions for Maths Class 12 Exercise 11.1

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.

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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).

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NCERT Solutions for Maths Class 12 Exercise 11.2

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