50.
Find the vector and the Cartesian equations for the line through the points A (3, 4, –7) and B (5, 1, 6).
The line passes through the points A (3, 4, –7) and B (5, 1,6).

where
are position vectors of A, B respectively.

Let
be the position vector of any point on the given line.
∴ the vector equation of the line is

or 
Taking 

Comparing the coefficients of
we get,


which is the Cartesian equation of line.
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