First slide

Scalars and Vectors

Question

The area of a parallelogram whose adjacent sides are $\vec{P} = 2 \hat{i} + 3 \hat{j}$ and $\vec{Q} = \hat{i} + 4 \hat{j}$ is

Moderate

A

5 square units
B

15 square units
C

20 square units
D

25 square units

Solution

$\vec{P} \times \vec{Q} = (2 \hat{i} + 3 \hat{j}) \times (\hat{i} + 4 \hat{j})$
            $= | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & 0 \\ 1 & 4 & 0 \end{matrix} |$
            $= \hat{i} (0 - 0) + \hat{j} (0 - 0) + \hat{k} (8 - 3) = 5 \hat{k}$
   $∴$ Area of parallelogram
    $= | \vec{P} \times \vec{Q} | = 5$ square units

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