Board Questions for Lines and Planes                              3/6 

(Below listed questions carries 3 Marks each)

March – 2010

1) Find the equation of line in Cartesian form passing through the point (3 , 2, -1)   and perpendicular to the vector 3i – 4j + 5k and i – j + k.

2) Find the Cartesian equation of the plane passing through the point (1 , 1 , 1) ,

(2 , 4 , 3) and (3 , 9 , 7) using vector method .

September – 2010

1) Find the vector equation and Cartesian equation of the line passing through two points (1 , -2 , 1) and (0 , -2 , 3) .

2) Find the angles between the planes r.(2i – j +k) = 6 and r.(i + j + 2k) = -9 .

September – 2009

1) Find the vector equation of line passing through the point i + 2j – 3k and perpendicular to the vector 2i + 3j + k and i – j + 4k .

2) A is (-1 , 1 , 2) and B is (5 , -3 , 4), find the equation of plane in vector and Cartesian form which passes through mid-point of seg AB and perpendicular to line AB .

March – 2008

1) By vector method, find the equation of line passing through the point

A (2 , -3 , -4) and parallel to OB, where O is the origin and B (2 , -2 , -1) .

2) By vector method, find the equation of plane passing through the point

A (1 , -1 , 1) which is parallel to the vectors 2i – j – k and 7i + j – 3k .

September – 2008

1) Using vector method, find the equation of line passing through the point

A (3 , 2 , -1) and B (4 , -1 , 3). Also write the equation in Cartesian form .

2) Find the vector equation of plane passing through the point (2 , 2 , -1) ,

(3 , 4 , 1) and (7 , 0 , 6) .  

By: Nazim Shaikh