A vector which bisects the angle between a¯=3i¯−4k¯ and b¯=5 j^+12k¯ is

a¯=5,b¯=13OP¯=55j¯+12k¯+133i¯−4j¯5+13=39i¯+25j¯+8k¯18

A vector which bisects the angle between a¯=3i¯−4k¯ and b¯=5 j^+12k¯ is

a¯=5,b¯=13OP¯=55j¯+12k¯+133i¯−4j¯5+13=39i¯+25j¯+8k¯18

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A vector which bisects the angle between $\bar{a} = 3 \bar{i} - 4 \bar{k}$ and $\bar{b} = 5 \hat{j} + 12 \bar{k}$ is

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$3 \bar{i} + 5 \bar{j} + \frac{8}{5} \bar{k}$

$39 \bar{i} - 25 \bar{j} + 8 \bar{k}$

$39 \bar{i} + 25 \bar{j} + 8 \bar{k}$

$3 \bar{i} - 5 \bar{j} + \frac{8}{5} \bar{k}$

answer is B.

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Detailed Solution

$|\bar{a}| = 5, |\bar{b}| = 13$

$\bar{O P} = \frac{5 (5 \bar{j} + 12 \bar{k}) + 13 (3 \bar{i} - 4 \bar{j})}{5 + 13}$

$= \frac{39 \bar{i} + 25 \bar{j} + 8 \bar{k}}{18}$

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A vector which bisects the angle between a¯=3i¯−4k¯ and b¯=5 j^+12k¯ is

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A vector which bisects the angle between $\bar{a} = 3 \bar{i} - 4 \bar{k}$ and $\bar{b} = 5 \hat{j} + 12 \bar{k}$ is