If the position vector of A and B are 2i¯+3j¯−k¯ and i¯−j¯+2k¯ respectively, then the unit vector of BA¯ and in the direction of AB¯ is

AB¯=(−1,−4,3) |AB¯|=26Unit vector =AB¯|AB|=126(−i¯−4j¯+3k¯)

If the position vector of A and B are 2i¯+3j¯−k¯ and i¯−j¯+2k¯ respectively, then the unit vector of BA¯ and in the direction of AB¯ is

AB¯=(−1,−4,3) |AB¯|=26Unit vector =AB¯|AB|=126(−i¯−4j¯+3k¯)

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If the position vector of A and B are $2 \bar{i} + 3 \bar{j} - \bar{k}$ and $\bar{i} - \bar{j} + 2 \bar{k}$ respectively, then the unit vector of $\bar{B A}$ and in the direction of $\bar{A B}$ is

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$\frac{1}{\sqrt{22}} (3 \bar{i} - 4 \bar{j} + 3 \bar{k})$

$\frac{1}{\sqrt{26}} (- \bar{i} - 4 \bar{j} + 3 \bar{k})$

$\frac{1}{\sqrt{26}} (- 3 \bar{i} - 4 \bar{j} + \bar{k})$

$\frac{1}{\sqrt{14}} (3 \bar{i} + 2 \bar{j} + \bar{k})$

answer is B.

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Detailed Solution

$\bar{A B} = (- 1, - 4, 3) | \bar{A B} | = \sqrt{26}$
Unit vector $= \frac{\bar{A B}}{| A B |} = \frac{1}{\sqrt{26}} (- \bar{i} - 4 \bar{j} + 3 \bar{k})$

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If the position vector of A and B are 2i¯+3j¯−k¯ and i¯−j¯+2k¯ respectively, then the unit vector of BA¯ and in the direction of AB¯ is

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If the position vector of A and B are $2 \bar{i} + 3 \bar{j} - \bar{k}$ and $\bar{i} - \bar{j} + 2 \bar{k}$ respectively, then the unit vector of $\bar{B A}$ and in the direction of $\bar{A B}$ is