Question

Figure shows the orientation of two vectors u and v in the XY plane.If $u=a\hat{i}+b\hat{j}$ and $v=p\hat{i}+q\hat{j}$ which of the following is correct?

• A. $a$ and $p$ are positive while $b$ and $q$ are negative
• B. $a,p$ and $b$ are positive while $q$ is negative
• C. $a,q$ and $b$ are positive while $p$ is negative
• D. $a,b,p$ and $q$ are all positive

Answer 1

The correct option is B $a,p$ and $b$ are positive while $q$ is negative

Here, for $\overrightarrow{u}$, the tail is placed at the origin and both the $x$-component and $y$-component have projection on positive $x$-axis and $y$-axis respectively. Therefore, $a$ and $b$ are positive. Next, we translate $\overrightarrow{v}$ in such a way that its direction is unchanged and its tail is placed at the origin. We will observe that the $x$-component has projection on positive $x$-axis, whereas, the $y$-component has projection on the negative $y$-axis. Therefore, $p$ is positive but $q$ is negative.

Hence, B is the correct answer.