1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Which of the following is/are a unit vector for all values of θ ?

A
(cosθ)^i(sinθ)^j
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(sinθ)^i+(cosθ)^j
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(sin2θ)^i(cosθ)^j
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(cos2θ)^i(sin2θ)^j
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D (cos2θ)^i−(sin2θ)^jWe know, unit vector has magnitude equal to 1. a:(cosθ)^i−(sinθ)^j magnitude=√cos2θ+sin2θ=1 ∀ θ∈R So, a unit vector. b:(sinθ)^i+(cosθ)^j magnitude=√sin2θ+cos2θ=1 ∀ θ∈R So, a unit vector. c:(sin2θ)^i−(cosθ)^j magnitude=√sin22θ+cos2θ≠1 for all θ∈R so, not a unit vector. d:(cos2θ)^i−(sin2θ)^j magnitude=√cos22θ+sin22θ=1 ∀ θ∈R so, a unit vector.

Suggest Corrections
1
Join BYJU'S Learning Program
Join BYJU'S Learning Program