Find a vector from its cross product and dot product with a given vector

1. A.
   $\frac{C\vec{A}+\vec{A}\times\vec{B}}{|\vec{A}|^2}$
2. B.
   $\frac{C\vec{A}\times\vec{B}}{|\vec{A}|^2}$
3. C.
   $\frac{C\vec{A}-\vec{A}\times\vec{B}}{|\vec{A}|^2}$
4. D.
   $\frac{C\vec{A}+\vec{B}}{|\vec{A}|^2}$

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

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

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

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

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1. A.
   $\sqrt{55}$
2. B.
   $\sqrt{155}$
3. C.
   $\sqrt{138}$
4. D.
   $\sqrt{170}$

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1. A.
   $\ \frac{5}{3}\widehat{i} + \frac{2}{3}\widehat{j} + \frac{2}{3}\widehat{k}$
2. B.
   $\widehat{i} - 2\widehat{j} + 4\widehat{k}$
3. C.
   $\widehat{i} + 2\widehat{k}$
4. D.
   $\ 2\widehat{i} - 3\widehat{j} + 4\widehat{k}$

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

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1. A.
   $\dfrac{\bar{b} \times \bar{c} - \beta\bar{b}}{|\bar{b}|^2}$
2. B.
   $\dfrac{\bar{b} \times \bar{c} - \beta\bar{c}}{|\bar{b}|^2}$
3. C.
   $\dfrac{\bar{b} \times \bar{c} + \beta\bar{b}}{|\bar{b}|^2}$
4. D.
   $\dfrac{\bar{b} \times \bar{c} + \beta\bar{c}}{|\bar{b}|^2}$

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