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Question

Mathematics Question on Vector Algebra

If α→sα→s a nonzero vector of magnitude ′α′'α' and λλ a nonzero scalar,then λα⃗λ\vec{α} is unit vector if

A

λ=1λ=1

B

λ=−1λ=-1

C

α=∣λ∣α=|λ|

D

α=1∣λ∣α=\frac{1}{|λ|}

Answer

α=1∣λ∣α=\frac{1}{|λ|}

Explanation

Solution

Vector λα⃗λ\vec{α} is a unit vector if ∣λα⃗∣=1.|λ\vec{α}|=1.
Now,
∣λα⃗∣=1.|λ\vec{α}|=1.
⇒∣λ∣∣α⃗∣=1⇒|λ||\vec{α}|=1
⇒∣α⃗∣=1∣λ∣[λ≠0]⇒|\vec{α}|=\frac{1}{|λ|} [λ\ne0]
⇒α=1∣λ∣[∣a⃗∣=a]⇒α=\frac{1}{|λ|} [|\vec{a}|=a]
Hence,vector λα⃗λ\vec{α} is a unit vector if α=1∣λ∣.α=\frac{1}{|λ|}.
The correct answer is D.