The Dot Product and the Angle Between Vectors Worksheet with Answer Key

What's on the worksheet

1. Let u = 3, -4, v = -2, 5 and w = 6, 1.
   \mathbf{u} \cdot \mathbf{v}\mathbf{v} \cdot \mathbf{w}\mathbf{u} \cdot (\mathbf{v} + \mathbf{w})(2\mathbf{u}) \cdot (-3\mathbf{w})\mathbf{w} \cdot \mathbf{w}
2. Find the angle between each pair of vectors, in degrees.
   \langle 2, 2 \rangle and \langle 0, 5 \rangle\langle -3, 1 \rangle and \langle 1, 2 \rangle\langle 1, \sqrt{3} \rangle and \langle -3, 3\sqrt{3} \rangle\langle 5, -2 \rangle and \langle -4, 3 \rangle
3. Vectors u and v have \|u\| = 4, \|v\| = 3 and u · v = 6.
4. Vectors u and v have \|u\| = 2 and \|v\| = 5, and (2u + v) · (u - 3v) = -92.
5. Vectors u and v have \|u\| = 3 and \|u + v\| = 3 √(3), and the angle between u and v is 2 π3 radians.
6. Let u = t, 3 and v = t, -1, where t is a real number.
7. A triangle has vertices A(-1, 0), B(5, 2) and C(1, 3).