Question

If θ is the angle between two vectors $\vec a$ and $\vec b$, then $\vec a.\vec b$≥0 only when

• A. 0<θ<$\frac{\pi}{2}$
• B. 0≤θ≤$\frac{\pi}{2}$
• C. 0<θ<π
• D. 0≤θ≤π

Answer 1

Answer: (B)

0≤θ≤$\frac{\pi}{2}$

Answer 2

Let θ be the angle between two vectors $\vec a$ and $\vec b$.
Then, without loss of generality,$\vec a$ and $\vec b$ are non-zero vectors so that |$\vec a$|and |$\vec b$|are positive.
It is known that $\vec a$.$\vec b$=|$\vec a$||$\vec b$|cosθ.
∴$\vec a$.$\vec b$≥0
⇒ |$\vec a$||$\vec b$|cosθ≥0
⇒ cosθ≥0 [|$\vec a$|and|$\vec b$|are positive]
⇒ 0≤θ≤$\frac{\pi}{2}$
Hence,$\vec a$.$\vec b$≥0 when 0≤θ≤$\frac{\pi}{2}$.
The correct answer is B.