Home Work Set # 1, Physics 217, Fall 2001
Due: September 12, 2001
1. Determine the angle between the body diagonals of a
2. Prove the BAC-CAB rule (Griffiths, equation (1.17)) by writing
out both sides in component form.
3. Find the transformation matrix
that describes a rotation by 120° about an axis from the origin
through the point (1, 1, 1). The rotation is clockwise as you look down the
axis toward the origin.
4. a) If
are two vector functions, what does the expression
mean ? (That is, what are the x
, and z
in terms of the Cartesian components of
Check the following product rule by calculating each term
5. The height of a certain hill (in feet) is given by
where y is the distance (in miles) north, and x is the
distance east of South Hadley.
a) Where is the top of the hill
b) How high is the top of the hill?
c) How steep (in feet per
mile) the hill at a point 1 mile north and 1 mile east of South Hadley? In what
direction is the slope steepest, at that point?
6. a) Calculate the
divergence of the following vector function:
b) Calculate the Laplacian of the following scalar function:
c) Calculate the Laplacian of the following vector function:
7. Show that
for a scalar function t
and a vector function