Texts:
Problem 1: Find the angle between the two vectors in the figure.
(0,0,1)
(0,1,0)
Problem 2: Prove the following formula for any four vectors ABCD = ACBD - ADBC.
001
Problem 3: Calculate the gradient of the function f(x,y,z) = xy^3/4 at the point (1,2,3).
Problem 4: For the vector function F = xy + 2yz + 3zx:
a) Calculate its divergence at the point (3,2,1).
b) Calculate its curl at the point (3,1,0).
Problem 5: Given the vector function v = x^2 + 2xy + y^2 + 2yz:
a) Calculate its surface integral over the six faces of the cube in the figure over a volume.
Problem 6: Given the vector function F = 2x + 3y^2 + 4y:
a) Calculate its surface integral.
