September 25, 2015
1. Find the angle between the given vector and the plane:
(a) (2, 3, 5) and 2x + 3y 4 = 2z
(b) The vector parallel to the line given by the symmetric equations
4y + 2
3x 5 =
and the plane containing the points (1, 1, 1), (1, 2,
September 18, 2015
1. Find the equation of the plane that is perpendicular to the plane 2x + 3y 4z = 1 and
intersects it along the line parallel to the vector v = (1, 2, 2). Find, also, the equation of the
line of intersection.
2. Find the intersection of
November 23, 2015
Due at the beginning of class on Wednesday after break.
Lengths of curves and areas of surfaces
1. Find the arc length of each curve. Draw each curve and describe in words its shape.
(a) r(t) = (4 + 3t, 2 2t, 5 + t), 3 t 4
(b) r(t) = (t,
October 23, 2015 (Due Friday October 30)
There are lots of topics on this one. Be sure to read through and ask me questions.
1. Find the directional derivatives of the given function f at the point p in the direction v. Also,
write the spaces X and Y so t
October 19, 2015 (Due Friday October 23)
1. I dont want you to forget old material. So, here are some review problems.
(a) Find the equation of the line passing through p = (1, 2, 1, 4) and normal to the hyperplane 3x 4y + 2z + 7w = 15. (Hint: a hyperplan