If a non-zero vector a is parallel to the line of intersection of the plane determined by the vectors the plane determined by the vectors then the angle between the vectors a and is
If three numbers are drawn at random successively without replacement from a set S = {1, 2, ... 10}, then the probability that the minimum of the chosen numbers is 3 or their maximum is 7
A.
(a) Total number of possible outcomes =10C3
Let A be the event that minimum of chosen number is 3 and B be the event that maximum of chosen number is 7 Then, n(A) = Number of ways of choosing remaining two numbers from the set{4, 5, 6, 7, 8, 9, 10} = 6c2 = 21 Similarly, n(B) = Number of ways of choosing remaining two numbers from the set{1, 2, 3, 4, 5, 6} = 6c2 = 15
and n(A B) = Number of ways of choosing remaining one number from the set {4, 5, 6} = 3c1 = 3
Thus, required probability
=
The equation of the plane through (4,4,0) and perpendicular to the planes 2x + y + 2z + 3 = 0 and 3x + 3y + 2z - 8 = 0
4x + 3y + 3z = 28
4x - 2y - 3z = 8
4x + 2y + 3z = 24
4x +2y - 3z = 24