$- A = - 2 i - - j + - k, - B = - i - - 3 j - - 5 k, - C = - 3 i - - 4 j - - 4 k$ are the vertices of a triangle.

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Solution

The correct option is C $R i g h t$ $a n g l e d$
$| A B | = \sqrt{(2 - 1)^{2} + (- 1 + 3)^{2} + (1 + 5) 2}$
$= \sqrt{1 + 4 + 36} = \sqrt{41}$
$| A C | = \sqrt{(2 - 3)^{2} + (- 1 + 4)^{2} + (1 + 4)^{2}}$
$= \sqrt{1 + 9 + 25}$
$= \sqrt{35}$
$| B C | = \sqrt{(1 - 3)^{2} + (- 3 + 4)^{2} + (- 5 + 4)^{2}}$
$= \sqrt{4 + 1 + 1}$
$= \sqrt{6}$
$∴ A B^{2} = A C^{2} + B C^{2}$
$41 = 35 + 6$
$41 = 41$
$∴$ This is a right angle triangle.

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Similar questions

A (2 \hat{i} - \hat{j} + \hat{k}), B (\hat{i} - 3 \hat{j} - 5 \hat{k}), C (3 \hat{i} - 4 \hat{j} - 4 \hat{k})

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 ˆ i - ˆ j + ˆ k, ˆ i - 3 ˆ j - 5 ˆ k

3 ˆ i - 4 ˆ j - 4 ˆ k

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

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

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