121. ABCD is quadrilateral, the co-ordinates of whose vertices are A (-1, 3, 2), B (3, -5, 4), C (5, -1, 0) and (-3, 1, 6). Show that mid-points of sides AB, BC, CD and DA form a parallelogram.

If  are the vertices of triangle ABC, then prove that its centroid G is 

The number of common tangent to the circles x²+y²-4x-6y-12=0 and x²+y²+6x+18y+26 = 0 is

• 1

• 2

• 3

• 3

The angle between the lines whose direction cosines satisfy the equations l +m+n=0 and l² = m²+n² is

• π/3

• π/4

• π/6

• π/6

If PS is the median of the triangle with vertices P(2,1), Q(6,-1) and R (7,3), then equation of the line passing through (1,-1) and parallel to PS is

• 4x-7y - 11 =0

• 2x+9y+7=0

• 4x+7y+3 = 0

• 4x+7y+3 = 0

Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4ax +2ay +c= 0 and 5bx +2by +d = 0 lies in the fourth quadrant and is equidistant from the two axes, then

• 2bc-3ad =0 

• 2bc+3ad =0

• 2ad-3bc =0

• 2ad-3bc =0