If overline{OA} = 3hat{i} + hat{j} - hat{k},| | vedclass

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(B) Given $\overline{OA} = 3\hat{i} + \hat{j} - \hat{k}$.Direction ratios of $\overline{AB}$ are $1, -1, 2$. Let the vector $\overline{AB} = k(\hat{i}

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$\sqrt{35}$

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(B) Given $\overline{OA} = 3\hat{i} + \hat{j} - \hat{k}$.Direction ratios of $\overline{AB}$ are $1, -1, 2$. Let the vector $\overline{AB} = k(\hat{i} - \hat{j} + 2\hat{k})$ for some scalar $k$.We know $|\overline{AB}| = |k| \sqrt{1^2 + (-1)^2 + 2^2} = |k| \sqrt{6}$.Given $|\overline{AB}| = 2\sqrt{6}$,so $|k|\sqrt{6} = 2\sqrt{6} \implies |k| = 2$.Thus,$\overline{AB} = 2(\hat{i} - \hat{j} + 2\hat{k}) = 2\hat{i} - 2\hat{j} + 4\hat{k}$ or $\overline{AB} = -2\hat{i} + 2\hat{j} - 4\hat{k}$.Since $\overline{OB} = \overline{OA} + \overline{AB}$,we have two cases:Case $1$: $\overline{OB} = (3\hat{i} + \hat{j} - \hat{k}) + (2\hat{i} - 2\hat{j} + 4\hat{k}) = 5\hat{i} - \hat{j} + 3\hat{k}$.Then $|\overline{OB}| = \sqrt{5^2 + (-1)^2 + 3^2} = \sqrt{25 + 1 + 9} = \sqrt{35}$.Case $2$: $\overline{OB} = (3\hat{i} + \hat{j} - \hat{k}) + (-2\hat{i} + 2\hat{j} - 4\hat{k}) = \hat{i} + 3\hat{j} - 5\hat{k}$.Then $|\overline{OB}| = \sqrt{1^2 + 3^2 + (-5)^2} = \sqrt{1 + 9 + 25} = \sqrt{35}$.In both cases,$|\overline{OB}| = \sqrt{35}$.

If $\overline{OA} = 3\hat{i} + \hat{j} - \hat{k}$,$|\overline{AB}| = 2\sqrt{6}$ and the direction ratios of $\overline{AB}$ are $1, -1, 2$,then $|\overline{OB}| = $

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