Question

Let the vectors $\vec a \ and \vec b$ be such that $\arrowvert \vec a \arrowvert=3 \ and \arrowvert \vec b \arrowvert=\frac{\sqrt{2}}{3}$ , then is a unit vector, if the angle between $\vec a \ and \vec b$ is
(A) π/6
(B) π/4
(C) π/3
(D) π/2

Answer 1

As per as questions, There are two vectors |a| and |b|.

|a| = 3 and |b| = √2/3

Now, It is not clearly mentioned that we need to add them or multiply them. Also, Unit vector is said which can be obtained in Cross product also and in addition also.  Let do this question from the view of Cross Product.

a × b = |a||b|Sinθ

∴ 1 = 3 × √2/3 Sinθ

∴ Sinθ = 1/√2

∴ Sinθ = Sin(π/4)

∴ θ = πn + (-1)ⁿα

When n = 0

θ = π/4

When n = 1,

θ = π - π/4 = 3π/4

When n = 2,

then, θ = 2π + π/4 = 9π/4

This is beyond 360.

That's why, there can be two angles between these vectors. They are, 45 or 135.

Now, As per as Option, the answer will be Option (B). 45°.

Hope it helps.