Find the vector equation of the line passing through the point (1, 2, – 4) and perpendicular to the two lines:
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)
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
Now, putting the value of & in formula
Therefore, the equation of the line is