Point where the bisector of angle A meets BC, and the length of the bisector

1. A.
   $(2 + 3\sqrt{2})\hat{i} + (3 + 3\sqrt{3})\hat{j} + 6\hat{k}$
2. B.
   $(2 - 3\sqrt{2})\hat{i} + (3 + 3\sqrt{2})\hat{j} + 6\hat{k}$
3. C.
   $(2 - 3\sqrt{2})\hat{i} + (3 - 3\sqrt{2})\hat{j} + 6\hat{k}$
4. D.
   $(2 - 3\sqrt{2})\hat{i} + (3 + 3\sqrt{2})\hat{j} - 6\hat{k}$

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1. A.
   $-5(\sqrt{2} + 1)$
2. B.
   $5(1 - \sqrt{2})$
3. C.
   $5(\sqrt{2} + 1)$
4. D.
   $5(\sqrt{2} - 1)$

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1. A.
   $15/2$
2. B.
   $11/2$
3. C.
   $1/4$
4. D.
   $\dfrac{3}{4}\sqrt{10}$

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1. A.
   $\dfrac{1}{3}\hat{i} + \dfrac{4}{3}\hat{j}$
2. B.
   $\dfrac{2}{3}\hat{i} + \dfrac{4}{3}\hat{j}$
3. C.
   $\dfrac{1}{3}\hat{i} + \dfrac{2}{3}\hat{j}$
4. D.
   $\dfrac{2}{3}\hat{i} + \dfrac{5}{3}\hat{j}$

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1. A.
   $\dfrac{2\sqrt{30}}{5}$
2. B.
   $\dfrac{2}{3}$
3. C.
   $\dfrac{\sqrt{13}}{5}$
4. D.
   $1$

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