Short Answer TypeFind the coordinates of the point, where the line 
intersects the plane 
. Also find the angle between the line and the plane.
Find the vector equation of the plane which contains the line of intersection of the planes. 
and 
and which is perpendicular to the plane 
A speaks truth in 60% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A?
Long Answer TypeUsing integration, find the area bounded by the curve x2 = 4y and the line x = 4y – 2.
The shaded area OBAO represents the area bounded by the curve x2 = 4y and the line x = 4y – 2.
Let A and B be the points of intersection of the line and parabola.
Co-ordinates of point A are 
Co-ordinates of point B are (2, 1).
Area OBAO = Area OBCO + Area OACO ...(1)
Area OBCO = 
Area OACO =
Therefore, required area = 
are two vectors such that 
then prove that vector 
is perpendicular to vector 
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