First slide

Scalars and Vectors

Question

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

Easy

A

Zero
B

Along west
C

Along east
D

Vertically downward

Solution

Direction of vector A is along z-axis
$∴ \vec{A} = a \hat{k}$
Direction of vector B is towards north
$\begin{array}{l} ∴ \vec{B} = b \hat{j} \\ Now \vec{A} \times \vec{B} = a \hat{k} \times b \hat{j} = a b (- \hat{i}) \end{array}$
$∴ The direction is \vec{A} \times \vec{B} is along west.$

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