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?
Let the probability that A and B speak truth be P(A) and P(B) respectively.
Therefore, 
A and B can contradict in stating a fact when one is speaking the truth and other is not speaking the truth.
Case 1: A is speaking the truth and B is not speaking the truth.
Case 2: A is not speaking the truth and B is speaking the truth.
Required Probability = 
Percentage of cases in which they are likely to contradict in stating the same fact =
From case 1, it is clear that is not necessary that 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.
are two vectors such that 
then prove that vector 
is perpendicular to vector 
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