Question

Figure shows the orientation of two vectors $\vec{u}$ and $\vec{v}$ in the $xy$ plane. If $\vec{u}=a\hat{i}+b\hat{j}$ and $\vec{v}=p\hat{i}+q\hat{j}$.
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

Answer: (B)

As per figure, in $\vec{u}=a\hat{i}+b\hat{j}$, both $a$ and $b$ are positive while in $\vec{v}=p\hat{i}+q\hat{j}$, $p$ is positive and $q$ is negative. Thus $a$, $b$ and $p$ are positive and $q$ is negative.