Observe that the given vector field is a gradient field:
Let , so that
Integrating the first equation with respect to , we get
Differentiating this with respect to gives
Now differentiating with respect to
gives
Putting everything together, we find a scalar potential function whose gradient is ,
It follows that the curl of is 0 (i.e. the zero vector).
Answer:
<u>Assuming b = 9.3i + 9.5j</u> <em>(b = 931 + 9.5 is wrong):</em>
a) a×b = 34.27k
b) a·b = 128.43
c) (a + b)·b = 305.17
d) The component of a along the direction of b = 9.66
Explanation:
<u>Assuming b = 9.3i + 9.5j</u> <em>(b = 931 + 9.5 is wrong)</em> we can proceed as follows:
a) The vectorial product, a×b is:
b) The escalar product a·b is:
c) <u>Asumming (a</u><u> </u><u>+ b)·b</u> <em>instead a+b·b</em> we have:
d) The component of a along the direction of b is:
I hope it helps you!