Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let the unit vector 
& 
are perpendicular and the moduli vector 
inclined at an angle α to 
& 
. If 
= λ 
+ m 
+ n( 
+ 
) then
A
λ = m
B
n 2 = 1 – 2 λ 2
C
n 2 = – cos 2 α
D
m 2 = 
Text Solution
Verified by ExpertsThe correct answer is:
A
(a, b, c, d)
= 
= 
=1
angle between 
and 
= angle between 
and 
⇒ 
= 
= cos α ( 
= 
= 
= 1)
also 
⇒ 
= 0
so 
∴ 
= λ = cos α , 
= cos α = m
Now | 
| = 1 ⇒ 
= 1 = 2 λ 2 + n 2 | 
| 2 ⇒ m = λ = cos α
⇒ 1 = 2 λ
2 + n 2 ⇒ n 2 = 1 – 2 λ 2 = 1 – 2cos 2 α
= –cos2 ⇒ λ 2 = m 2 = 
= 
Hence all are correct.
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