Short Answer TypeThe scalar product of the vector 
with a unit vector along the sum of vectors 
is equal to one. Find the value of 
and hence find the unit vector along 
An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.
An experiment succeeds as often as it fails.
Therefore, there are 3 successes and 1 failures.
Thus the probability of success 
And the probability of failure = 
We need to find the probability of atleast 3 successes in the next five trials.
Required Probability = P(X= 3) + P(X = 4) + P(X = 5)
Find the value of p, so that the lines:
are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, -4) and parallel to line l1.
Long Answer TypeFind the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x- y + z = 0. Also find the distance of the plane obtained above, from the origin.
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