Table of Contents
Chapter 27 Direction Cosines and Direction Ratios Exercise Ex. 27.1
Question 1
If a line makes angles of 90°, 60° and 30° with the positive direction of x,y and z-axis respectively, find its direction cosines.Solution 1
Let l, m and n be the direction cosines of a line.
l = cos 90° = 0
Question 2
If a line has direction ratios 2, -1, -2, determine its direction cosines.Solution 2
Question 3
Find the direction cosines of the line passing through two points (-2, 4, -5) and (1, 2, 3).Solution 3
Question 4
Using direction ratios show that the points A (2, 3, -4), B (1, -2, 3) and C (3, 8, -11) are collinear.Solution 4
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 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Find the acute angle between the lines whose direction ratios are proportional to 2:3:6 and 1:2:2.Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16(i)
Solution 16(i)
Question 16(ii)
Solution 16(ii)
Question 16(iii)
Solution 16(iii)
Question 16(iv)
Find the angle between the lines whose direction cosines are given by equations
2l + 2m – n = 0, mn + ln + lm = 0Solution 16(iv)
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