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 
Short Answer TypeShow that the four points A, B, C and D with position vectors
respectively are coplanar.
Given position vectors of four points A, B, C and D are:
These points are coplanar, if the vectors, 
are coplanar. 
These vectors are coplanar if and only if, they can be expressed as a linear combination of other two.
So Let
Comparing the coefficients, we have, 
These values of x and y satisfy the equation 3x + 3y = -2.
Hence the vectors are coplanar.
are parallel.
write the vector equation for the line. 
, find the value of a.
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