1. Calculate the directional derivative of the function :

(, , ) = ^2 + ^3

At the point (1, 1,1) in the direction of (3,1, 1).

2. A particle moves along the curve:

=2t^2 =t^24 and =3t5,

Where is the time. Find the components of its velocity and acceleration

at time = 1, in the direction 3 + 2k

3. show that the vector =(+3)+(3)+(2) is solenoidal.

4. determine the constant a, b, and c so that: = ( + 2 + ) + ( 3 ) (4 + + 2), is irrotational