Question

What is the angle between the two vectors shown in the figure?

• A. $\theta$
• B. $\frac{\theta }{2}$
• C. $\pi -\theta$
• D. $\theta -\pi$

Answer 1

The correct option is C $\pi -\theta$

A bit confused? Don’t worry. Look when two vectors are represented by two directed line segments, then the angle between them is the angle between those line segments when their initial points are same In the given figure terminal point of $\underset{AB}{\to }$ is the initial point of $\underset{BC}{\to }$.
So terminal point of one vector is joined to the initial point of another vector

Now let’s draw it like this

What we have done is we have shifted $\underset{AB}{\to }$ in the same direction to make sure that initial points of both the vectors are joined. Now the angle between these two line segments will be the angle between two vectors.
The angle is $(\pi -\theta )$ as shown in the figure