3-D Geometry: Plane

1.    The equation of the plane through  (2, 3, – 4) and (1 – 1, 3) and parallel to x-axis is
    (a)    7y – 4z – 5 = 0    (b)    4y – 7z – 5 = 0
    (c)    4y + 7z + 5 = 0    (d)    7y + 4z – 5 = 0
Ans. 1 (d)

2.     If from a paint P (a, b, c) perpendicular PA P B and to yz and zx planes, then the equation of the plane OAB is
    (a)    bcx + cay + abz = 0    (b)    bcx + cay – abz = 0
    (b)    bcx – cay + abz = 0    (d)    – bcx + cay + abz = 0
Ans. 2 (b)

3.    The equation of the plane which bisects the line joining the point (3, 2, 2), (5, 4, 6) at right angles  is
    (a)    x + y + 2z – 15 = 0    (b)    x + 2y + z – 15 = 0
    (c)    2x + y + z – 15 = 0    (d)    x + y + z – 8 = 9
Ans. 3 (a) 

4.    The foot of perpendicular drawn from the paint (1, 3, 4) to the plane 2x – y + z = – 3 is
    (a)    (1, 2, 3)                 (b)    (5, 7, 17)
    (c)    (5/3, – 7/3, 17/3)    (d)    (– 5/3, 7/3, 17/3)   
Ans.  4 (d)

5.    The two points (1, 1, 1) and (– 3, 0, 1) with respect to the plane 3x + 4y – 12z + 13 = 0 lie on
    (a)    Opposite side    (b)    Same side
    (c)    On the plane     (d)    None of these

Ans. 5 (a)