Name: _________________
Dot Products
Reading Assignment: 1.3
Recommended exercises: 1 – 12 (some), 15, 17, 22, 26, 28
1) If a = 2i - 3j + 6k and b = 4i + 2j + 4k, find a b and the angle between a and b to the
nearest degree. Find projab.
2) Find the interior angles of the triangle whose vertices are (1, 0, 2), (2,1, 1), and (1, 2, 2) .
3) Find three non-parallel non-zero vectors orthogonal to a above.
Name: _________________
4) Find z so that i + j + zk makes an angle of sixty degrees with b = 4i + 2j + 4k. Find q
to minimize the angle between i + j + qk and b.
5) Find the angle between an edge of a cube and one of the long diagonals.
6) A vector originating at the origin makes an angle of 75 with the positive x-axis, and
35 with the positive y-axis. What angle does it make with the z-axis?
Name: _________________
7) Let a = (1,4) and b = (1,3) . Find projab and projba, then sketch all 4 vectors on the
coordinate plane below.
y
5
x
-1
-5
5
8) Show that the vector v u  u v bisects the angle between u and v .