A line passing through the point A with position vector  is parallel to the vector  Find the length of the perpendicular drawn on this line from a point p with vector 

23.

If 

Evaluate: 

Three schools X, Y, and Z organized a fete (mela) for collecting funds for flood victims in which they sold hand-held fans, mats and toys made from recycled material, the sale price of each being Rs. 25, Rs. 100 andRs. 50 respectively. The following table shows the number of articles of each type sold:
School/Article                     School X                   School Y                School Z
Hand-held fans                         30                         40                         35
      Mats                                  12                         15                         20
       Toys                                 70                         55                         75
Using matrices, find the funds collected by each school by selling the above articles and the total funds collected. Also write any one value generated by the above situation. 

Sketch the region bounded by the curves  and find its area using integration. 

Find the particulars solution of the differential equation  given that y =1 when x = 1.

Find the particulars solution of the differential equation 

Show that lines:

Also, find the equation of the plane containing these lines.