Orthogonal Vectors Worksheet with Answer Key

What's on the worksheet

1. Decide whether the two vectors are orthogonal.
2. Find every value of k for which the two vectors are orthogonal.
   \langle k, k + 1 \rangle and \langle 4, -3 \rangle\langle k, k \rangle and \langle k - 2, 3 \rangle\langle 2k, 1 \rangle and \langle k, k - 3 \rangle
3. Let A(2, 2) and B(10, -4).
4. Use \|u ± v\|² = \|u\|² ± 2\,u · v + \|v\|².
5. The quadrilateral ABCD has vertices A(-1, -2), B(0, 5), C(5, 10) and D(4, 3).
6. Let A(3, -5) and B(7, -11), and let M be the midpoint of AB.