(i)Find the projection of 
on 
where 
= 
, 
= 
and 
= 
.
(ii)Find the projection of the line segment joining (2, – 1, 3) and (4, 2, 5) on a line which makes equal acute angles with co-ordinate axes.
(iii)P and Q are the points (–1, 2, 1) and (4, 3, 5) respectively. Find the projection of PQ on a line which makes angles of 120º and 135º with y and z axes respectively and an acute angle with x-axis.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) 
(ii) 
(iii) 2 
– 2
Sol- (i) 
= 
= 
Projection of 
on 
= 
= 
= 
= 
(iii) m = cos 120° = 
2 + m 2 + n 2 = 1
⇒ 2 + 
⇒ 2 = 
⇒ = 
as acute angle with x-axis
∴ required projection = |(x 2 – x 1 ) + (y 2 – y 1 ) m + (z 2 – z 1 )n|
= |5 × 1/2 + 1 × (– 1/2) + 4 × (– 1/ 
) = 
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