Dot Product, Length and Orthogonality in N Dimensions Worksheet with Answer Key

What's on the worksheet

1. Compute each dot product, length or distance.
   (3, −1, 4, 2) · (2, 5, −1, 3)(1, −2, 0, 5, 3) · (4, 3, 7, −1, 2)\lVert (2, -1, 4, 2) \rVert\lVert (1, 3, -2, 2, 1) \rVert\lVert (0, 3, -1, 1, 2, -3) \rVert
2. Let v = (2, 2, -4, 5) in R^4.
3. Let u = (-2, x, -3, 0, -1) and v = (-3, 4, -4, -1, -4) in R^5.
4. Vectors u, v and w in some R^n have u = 2, v = 3, w = 1, u · v = 1, u · w = 0 and v · w = -2.
5. Let a = (1, 0, 2, 3, 1) and b = (3, 2, 0, 1, 1) in R^5.
6. In R^4, let d = (1, 1, 1, 1).