First slide

Vectors

Question

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

Moderate

A

5 square units
B

10 square units
C

20 square units
D

2.5 square units

Solution

Area = $\frac{1}{2} | \vec{P} \times \vec{Q} | = | \frac{1}{2} | (\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & 0 \\ 1 & 4 & 0 \end{matrix}) |$
= $| \frac{1}{2} [2 \times 4 - 3 \times 1] \hat{k} | = \frac{5}{2}$

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