First slide

Scalars and Vectors

Question

The area of the triangle formed by vectors $3 \hat{i} + 4 \hat{j}$ and $- 3 \hat{i} + 7 \hat{j}$ is

Moderate

A

8.5 units
B

12.5 units
C

14.5 units
D

16.5 units

Solution

Let $\bar{A} = 3 \hat{i} + 4 \hat{j}$ and $- 3 \hat{i} + 7 \hat{j}$
Now, $\bar{A} \times \bar{B} = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 4 & 0 \\ - 3 & 7 & 0 \end{matrix} | = 0 \hat{i} - 0 \hat{i} + [(7) (3) - (4) (- 3)] \hat{k} = 33 \hat{k}$
$\Rightarrow$ $Δ = \frac{1}{2} | \bar{A} \times \bar{B} | = \frac{33}{2} = 16.5 s q . u n i t s$ .

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