Equation of the line through a point perpendicular to two given lines or vectors

1. A.
   $\dfrac{x+1}{2} = \dfrac{y-3}{7} = \dfrac{z+2}{4}$
2. B.
   $\dfrac{x+1}{-2} = \dfrac{y-3}{-7} = \dfrac{z+2}{4}$
3. C.
   $\dfrac{x+1}{2} = \dfrac{y-3}{7} = \dfrac{z+2}{-4}$
4. D.
   $\dfrac{x+1}{2} = \dfrac{y-3}{-7} = \dfrac{z+2}{4}$.

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

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1. A.
   $\frac{x+3}{2}=\frac{y+1}{7}=\frac{z+2}{4}$
2. B.
   $\frac{x-3}{-2}=\frac{y-1}{7}=\frac{z-2}{4}$
3. C.
   $\frac{x-3}{2}=\frac{y-1}{-7}=\frac{z-2}{4}$
4. D.
   $\frac{x-3}{2}=\frac{y-1}{5}=\frac{z-2}{4}$

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1. A.
   $\vec{r}=(\hat{i}+2\hat{j}+3\hat{k})+\lambda(-4\hat{i}-7\hat{j}-13\hat{k})$
2. B.
   $\vec{r}=(\hat{i}+2\hat{j}+3\hat{k})+\lambda(-4\hat{i}+7\hat{j}-13\hat{k})$
3. C.
   $\vec{r}=(\hat{i}+2\hat{j}+3\hat{k})+\lambda(-4\hat{i}-7\hat{j}-13\hat{k})$
4. D.
   $\vec{r}=(\hat{i}+2\hat{j}+3\hat{k})+\lambda(4\hat{i}-7\hat{j}-13\hat{k})$

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1. A.
   $\bar{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(5\hat{i} + 4\hat{j} + 7\hat{k})$
2. B.
   $\bar{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k})$
3. C.
   $\bar{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(3\hat{i} + 7\hat{j} + 13\hat{k})$
4. D.
   $\bar{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(4\hat{i} + 10\hat{j} + 9\hat{k})$

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1. A.
   $\dfrac{x + 1}{2} = y + 2 = \dfrac{z + 3}{3}$
2. B.
   $\dfrac{x - 1}{2} = y - 2 = \dfrac{z - 3}{3}$
3. C.
   $\dfrac{x - 1}{2} = y - 2 = \dfrac{z - 3}{-3}$
4. D.
   $\dfrac{x + 1}{2} = y + 2 = \dfrac{z + 3}{-3}$

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