The Cartesian equations of a line are `(x-5)/3=(y+4)/7=(z-6)/2dot` Find a vector equation for the line.

Explanation

If a line is given by `frac{{x}-a}{1}=frac{y-b}{m}=frac{z-c}{n}=lambda` then vector equation of the line is given by


``
`vec{r}=a vec{i}+b vec{j}+c vec{k}+lambda(vec{l}+{m} vec{j}+{n} vec{k})`


``
Here `a=5, b=-4, c=6` and `l=3, m=7, n=-2`


Substituting the above values, we get


``
`vec{r}=5 vec{i}-4 vec{j}+6 vec{k}+lambda(3 vec{i}+7 vec{j}-2 vec{k})`


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