Q. 194.2( 34 Votes )
Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes s and .
The vector equation of a line passing through a point with position vector and parallel to a vector is
Given, the line passes through (1,2,3)
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
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