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