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.
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.
Find the distance of the point (2, 12, 5) from the point of intersection of the line 
Any point in the line is
The vector equation of the plane is given as
Thus, the point of intersection of the line and the plane is:
Distance between (2, 12, 5) and (14, 12, 10) is:
show that
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