The perimeter of a triangle with sides $3 i + 4 j + 5 k, 4 i - 3 j - 5 k$ and $7 i + j$

\sqrt{450}

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\sqrt{150}

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\sqrt{240}

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\sqrt{210}

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Solution

The correct option is A $\sqrt{450}$
$P e r i m e t e r = ∣ ∣ ∣ 3 \land i + 4 \land j + 5 \land k ∣ ∣ ∣ + ∣ ∣ ∣ 4 \land i - 3 \land j + 5 \land k ∣ ∣ ∣ + ∣ ∣ ∣ 7 \land i + \land j ∣ ∣ ∣$
$= \sqrt{9 + 16 + 25} + \sqrt{16 + 9 + 25} + \sqrt{49 + 1}$
$= \sqrt{50} + \sqrt{50} + \sqrt{50}$
$= 3 \sqrt{50}$
$= \sqrt{50 \times 9} = \sqrt{450}$

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