Question

A vector ${\overline{F}}_1$ is along the positive x- axis. If its cross product with another vector ${\overline{F}}_2$ is zero, then ${\overline{F}}_2$ could be:

• A. $4\hat{j}$
• B. $-4\hat{i}$
• C. $(\hat{i}+\hat{k})$
• D. $-(\hat{i}+\hat{j})$

Answer 1

The correct option is B $-4\hat{i}$

The vector product of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is defined by $\overrightarrow{A}\times \overrightarrow{B}=\hat{n}|A||B|\sin x$, where $\hat{n}$ is the unit vector perpendicular to both A and B vectors and x is the angle between them.
Here in this question the vector product of $\overrightarrow{P1}$ and $\overrightarrow{P2}$ vectors is zero. This is only possible in two cases: 1) Any of the vectors is zero itself or 2) the $\sin$ of the angle between them is zero.
From the given options, the vector parallel to the given vector $\hat{i}$ is $-4\hat{i}$.