The vector equation of a straight line passing through a fixed point with position vector a → and parallel to a given vector b → is. r → = a → + λ b →, where λ is scalar. Note : In the above equation r → is the position vector of any point P (x, y, z) on the line. Example : Find the equation of plane passing through the point i ^ + j ^ + k ^ and parallel to the plane r →. 2 i ^ – j ^ + 2 k ^ = 5.. Example: Find the equation of the plane containing the line of intersection of the planes x + y + z – 6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1, 1, 1), Solution : The equation of the plane through the line of intersection of the.