# NCERT Solutions For Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1

Here, Below you all know about NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Question Answer. I know many of you are confused about finding Chapter 11 Three Dimensional Geometry Ex 11.1 Of Class 12 NCERT Solutions. So, Read the full post below and get your solutions.

## NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1

NCERT TEXTBOOK EXERCISES

Ex 11.1 Class 12 Maths Question 1.
If a line makes angles 90°, 135°, 45° with the and z axes respectively, find its direction cosines.

Solution:

Direction angles are 90°, 135°, 45°
Direction cosines are

Ex 11.1 Class 12 Maths Question 2.
Find the direction cosines of a line which makes equal angles with coordinate axes.

Solution:

Let direction angle be α each
∴ Direction cosines are cos α, cos α, cos α
But l² + m² + n² = 1
∴cos² a + cos² a + cos² a = 1

Ex 11.1 Class 12 Maths Question 3.
If a line has the direction ratios – 18,12, -4 then what are its direction cosines?

Solution:

Now given direction ratios of a line are -8,12,-4
∴ a = -18,b = 12,c = -4
Direction cosines are

Ex 11.1 Class 12 Maths 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), C (5,8,7).
Let direction ratios of AB be

Ex 11.1 Class 12 Maths 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), C (-5, -5, -2)
(i) Direction ratios of AB are (-4,-4,6)
Direction cosines are

## NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11.1 PDF

For NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1, you may click on the link below and get your NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise pdf file.