First slide

Scalars and Vectors

Question

The area of the triangle whose vertices are A (1, -1, 2), B (2, 1, -1) and C (3, -1, 2) is (in area units)

Moderate

A

26
B

$7 \sqrt{13}$
C

$\sqrt{13}$
D

8

Solution

$\vec{AB} = \hat{i} + 2 \hat{j} - 3 \hat{k} \vec{BC} = \hat{i} - 2 \hat{j} + 3 \hat{k} \vec{AB} x \vec{BC} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 2 & - 3 \\ 1 & - 2 & 3 \end{matrix}| = - 6 \hat{j} - 4 \hat{k} \Rightarrow |\vec{AB} x \vec{BC}| = \sqrt{{(- 6)}^{2} + {(- 4)}^{2}} = \sqrt{52} unit \Rightarrow Area of ∆ = \frac{1}{2} |\vec{AB} x \vec{BC}| = \sqrt{13} unit$

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