The three vectors \vec{A} = 3\hat{i} - 2\hat{j} + \hat{k}, \vec{B} = \hat{i} - 3\hat{j} + 5\hat{k} and \vec{c} = 2\hat{i} + \hat{j} - 4\hat{k} form
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\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}
\(\left|\vec{A}\right| = \sqrt{3^2 + (-2)^2 + 1^2} = \sqrt{9 + 4 + 1} = \sqrt{14}\)
\(\left|\vec{B}\right| = \sqrt{1^2 + (-3)^2 + 5^2} = \sqrt{1 + 9 + 25} = \sqrt{35}\)
\(\left|\vec{A}\right| = \sqrt{2^2 + 1^2 + (-4)^2} = \sqrt{4 + 1 + 16} = \sqrt{21}\)
As \(\mathbf{B} = \sqrt{A^{2} + C^{2}}\)
Therefore, ABC will be right angled triangle.
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