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Fill in the blanks: The vector equation of the line \frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2} is __________.


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The equation of the line is given as


Clearly, the line passes through A (5, -4, 6) and has the direction ratios 3, 7, and 2.

Also, the position vector of A is \vec{a}=5\hat{i}-4\hat{j}+6\hat{k}

The direction vector of the given line will be:


Also, the vector equation of a line passing through the given point whose position vector is a and b is:

\vec{r}=\vec{a}+\lambda \vec{b}

Hence, the required equation of the line will be:

\vec{r}=\left ( 5\hat{i}-4\hat{j}+6\hat{k} \right )+\lambda\left ( 3\hat{i}+7\hat{j}+2\hat{k}\right )

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