The vector area of the triangle whose adjacent sides are $2 ¯ i + 3 ¯ j$ and $- 2 ¯ i + 4 ¯ j$ is

5 ¯ ¯ ¯ k

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7 ¯ ¯ ¯ k

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9 ¯ ¯ ¯ k

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11 ¯ ¯ ¯ k

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Solution

The correct option is B $7 ¯ ¯ ¯ k$
$\to n = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 2 & 3 & 0 - 2 & 4 & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 14^k$
Area vector $= \frac{1}{2} \to n = 7^k$

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2 \to i - \to j + \to k, \to i - 3 \to j - 5 \to k, - 3 \to i + 4 \to j + 4 \to k

2 \hat{i} - 4 \hat{j} - 5 \hat{k} and 2 \hat{i} + 2 \hat{j} + 3 \hat{k}

\vec{a} = 4 \hat{i} - 3 \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} - 4 \hat{j} + 5 \hat{k}, \vec{c} = \hat{i} - \hat{j}

2 \hat{i} - 4 \hat{j} + 5 \hat{k} and \hat{i} - 2 \hat{j} - 3 \hat{k} .

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