Dear friends,
Try please my competition tasks for my students.
23 june 2010
Vectors
Prove that if
, then
.
Pitagor theorem in 3D
Prove that if a, b and c are three mutually perpendicular
vectors in 3D, then:
(a x b)2 + (b x c)2 +
(c x a)2 =
[ (b - a) x (c - a) ] 2 .
7 june 2010
Multiplication of continuous matrixs
Let f = f(x,y) and g = g(x,y) are continuous functions in
D: x ∈ [0, 1] y ∈ [0, 1]
We define their "product" by equality:
Prove the associativity of this product among continuous functions in D.
Find such continuous function in D e = e(x,y) , satisfying conditions
for unit element for such product.
Stancho Pavlov