1. A
   $\frac{11}{4}$
2. B
   $-\frac{11}{4}$
3. C
   $\frac{11}{2}$
4. D
   $\frac{4}{11}$

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1. A
   $\bar{r}=\left(\frac{1}{2}\hat{i}-\frac{2}{3}\hat{j}+2\hat{k}\right)+\lambda\left(3\hat{i}+2\hat{j}+6\hat{k}\right)$
2. B
   $\bar{r}=\hat{i}-\hat{j}+\left(2\hat{i}+\hat{j}+\hat{k}\right)$
3. C
   $\bar{r}=\left(\frac{1}{2}\hat{i}-\hat{j}\right)+\lambda\left(\hat{i}-2\hat{j}+6\hat{k}\right)$
4. D
   $\bar{r}=\left(\hat{i}+\hat{j}\right)+\lambda\left(\hat{i}-2\hat{j}+6\hat{k}\right)$

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1. A
   $4,5,7$
2. B
   $4,-5,7$
3. C
   $4,-5,-7$
4. D
   $-4,5,8$

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1. A
   $3$
2. B
   $\sqrt{11}$
3. C
   $\sqrt{13}$
4. D
   $5$

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

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1. A
   $k=1$ or $-1$
2. B
   $k=0$ or $-3$
3. C
   $k=\pm 3$
4. D
   $k=0$ or $-1$

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1. A
   perpendicular
2. B
   intersecting
3. C
   skew
4. D
   coincident

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1. A
   $x=y=z$
2. B
   $y=z$
3. C
   $y=0,\ z=0$
4. D
   $x=0,\ y=0$

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1. A
   $45^\circ$
2. B
   $30^\circ$
3. C
   $0^\circ$
4. D
   $90^\circ$

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1. A
   $2,1,6$
2. B
   $2,1,-6$
3. C
   $2,-1,6$
4. D
   $-2,1,6$

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1. A
   $14$
2. B
   $196$
3. C
   $2\sqrt{14}$
4. D
   $\frac{\sqrt{14}}{2}$

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