Question

A vector $\overrightarrow{A}$ points vertically upward and $\overrightarrow{B}$ point towards north. The vector product $\overrightarrow{A}\times \overrightarrow{B}$ is

• A. zero
• B. along west
• C. along east
• D. vertically downwards

Answer 1

Answer: (B)

Step 1: Given

Direction of vector $\overrightarrow{A}$ is along $+z$ axis (upward) $\overrightarrow{A}=a\hat{k}$

Direction of vector $\overrightarrow{B}$ is towards north($+yaxis$) $\overrightarrow{B}=b\hat{j}$

Taking cross product of the vectors

Now $\overrightarrow{A}\times \overrightarrow{B}=a\hat{k}\times b\hat{j}=ab(-\hat{i})$

As we know that the cross product of the two vectors is always perpendicular to the both of the vectors.

Hence the direction of $\overrightarrow{A}\times \overrightarrow{B}$ is along west.