Short Answer Type
Long Answer TypeTwo schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award x each, y each and z each for the three respective values to 3, 2 and 1 students respectively with a total award money of 1,600. School B wants to spend 2,300 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount for one prize on each value is 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.
If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum when the angle between them is 
Let ABC be the right angle triangle with base b and hypotenuse h.
Given that b+ h = k
Let A be the area of the right triangle.
Differentiating the above function with respect to be, we have
For the area to be maximum, we have
Again differentiating the function in equation (1), with respect to b, we have
Now substituting 
in equation (2), we have
Thus area is maximum at 
Now, 
Let 
be the angle between the base of the triangle and the hypotenuse of the right angle. 
Short Answer TypeShow that the four points A, B, C and D with position vectors
respectively are coplanar.
Switch
are parallel.
write the vector equation for the line. 
, find the value of a.
