Find the vector and Cartesian equations of the line through the point `(5,\ 2,\ -4)` and which is pralel to the vector `3 hat i+2 hat j-8 k dot`

Explanation

The vector and cartesian equations of the line passing through the point `(5,2,-4)` and parallel to the vector `3 hat{i}+2 hat{j}-8 hat{j}` are


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`5 hat{i}+2 hat{j}-4 hat{k}+lambda(3 hat{i}+2 hat{j}-8 hat{k}) text { and } frac{x-5}{3}=frac{y-2}{2}=frac{z+4}{-8} text {. }`
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