If 

Evaluate: 

23.

Evaluate:

Evaluate:

Evaluate: 

If  are two vectors such that  then prove that vector  is perpendicular to vector 

Find 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?

Using integration, find the area bounded by the curve x² = 4y and the line x = 4y – 2.