Find the direction ratios and the direction cosines of the line segment joining the points:
(i) A (1, 0, 0) and B(0, 1, 1)
(ii) A(5, 6, -3) and B (1, -6, 3)
(iii) A (-5, 7, -9) and B (-3, 4, -6)
Given two line segments , we have the direction ratios,
Of the line joining these 2 points as,
AB = -
+ 
+ k, (direction ratio)
The unit vector in this direction will be the direction cosines, i.e.,
Unit vector in this direction is:- (-
+ 
+ k)/
The direction cosines are (
)
(ii) Given two line segments , we have the direction ratios,
Of the line joining these 2 points as,
AB = -4
+ (-12)
+ 6k
The direction ratio in the simplest form will be, (2, 6, -3)
The unit vector in this direction will be the direction cosines, i.e.,
Unit vector in this direction is:- (2
+ 6
-3k)/
The direction cosines are (
)
(iii) Given two line segments , we have the direction ratios,
Of the line joining these 2 points as,
AB = 2
- 3
+ 3k, (direction ratio)
The unit vector in this direction will be the direction cosines, i.e.,
Unit vector in this direction is:- (2
-3
+ 3k)/
The direction cosines are (
)