Hello Students. In this post, you will find the complete 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 α, m = cos β and n = cos γ. Here, α = 90°, β = 135°, γ = 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 α, m = cos β and n = cos γ. Here, α = β = γ.
Thus l = m = n =
cos α
But, l² + m² + n² = 1
∴
cos² α + cos² α +
cos² α = 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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