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 ()