Question

If $\overline{a}and\overline{b}$ are two vectors as shown in the figure, then $\overline{a}.\overline{b}$ will equal to $|\overline{a}||\overline{b}|cos\theta$

• A. True
• B. False

Answer 1

The correct option is B

False

We know that for two vectors $\overline{a}and\overline{b}$, the dot product $\overline{a}.\overline{b}$ is defined as $|\overline{a}||\overline{b}|cos\theta$ , where $\theta$ is the angle between the two vectors. This $\theta$ is the angle between two line segments representing the vectors when their initial points are same. In the given figure, the initial point of $\overline{b}$ is joined to terminal point of $\overline{a}$.

So the required angle would be $(\pi -\theta )$ as shown.

$So\overline{a}.\overline{b}=|\overline{a}||\overline{b}|cos(\pi -\theta )$

$=-|\overline{a}||\overline{b}|cos\theta$