298.
Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes 
Let a, b, c be the direction ratios of the line passing through the point (1, 2, 3).
∴ equation of line is
...(1)
The equations of planes are
and 
or 
and 
or 
...(2)
and 
...(3)
Since line (1) is parallel to the plane (2) whose direction ratios of the normal are 1, -1, 2.
∴ a (1) + b (– 1) + c (2) = 0
∴ a – b + 2c = 0
Again line (1) is parallel to the plane (2) whose direction ratios of the normal are 3,1,1.
∴ 3a + b + c = 0 .....(5)
From (4) and (5), we get,
∴ from (1), the equation of line is
which is vector equation of line.
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Short Answer Type
then find the value of k.
contains the line whose vector equation is 
lies in the plane 
whose vector equation is 
do not intersect each other. 
are coplanar. 
lies in the plane 
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