Answer :
The vector equation of a line passing through a point with position vector and parallel to a vector
is
⇒
Given, the line passes through (1, 2, -4)
So,
Given, line is parallel to both planes
∴ Line is perpendicular to normal of both planes.
i.e is perpendicular to normal of both planes.
we know that -
is perpendicular to both
&
So, is cross product of normals of planes
and
Required Normal
Thus,
Now, putting the value of &
in formula
Therefore, the equation of the line is
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