Cross Products
Reading Assignment: 1.4
Suggested problems: 1, 3, 5, 9, 11, 17, 19, 25, 26, 27 – 33 (some)
2
3 2
1) Calculate
7 9
2) Calculate 4
5
1 6
2
1
3
0
2 2 3 1
1 4 2 0
3) Calculate
3 2 0 1
0
3
0 4
4) Find the area of the parallelogram whose vertices are (1, 2, 1), (3,3, 2), (2, 2,1), and ( 6,3, 4)
5) Find a unit vector orthogonal to both (1, 0, 1) and (2, 2, -1)
6) Let v and w be vectors and k be a real number. Explain why v  w = v  (w + kv):
a) using algebraic properties.
b) using geometry (include an explanatory picture).
7) Find two non-parallel, nonzero vectors orthogonal to both of the four-dimensional vectors
(2,1,3, 4) and (1, 2, 0,1) . Try to make them orthogonal to each other, if you can! (Something to
think about: is there a way to tackle this kind of problem in general? In arbitrary dimensions?)
8) Use vectors to show that the diagonals of a parallelogram have the same length if and only if
the parallelogram is a rectangle.
a
b