Vectors in Space Worksheet with Answer Key

What's on the worksheet

1. For each pair of points in space, write PQ in component form and in i, j, k form, and find its magnitude exactly.
   P(-1, 2, 4) and Q(3, 10, 5)P(-2, 4, 0) and Q(1, 0, 12)P(5, -3, -1) and Q(4, -3, 2)
2. Find the unit vector in the direction of each vector, in the same notation as the vector.
   \langle -2, 3, 6 \rangle4\mathbf{i} - 4\mathbf{j} + 2\mathbf{k}\langle 1, -1, 2 \rangle-3\mathbf{j} + 3\mathbf{k}
3. Each pair of vectors in space is drawn from one tail.
   \langle 1, -1, 0 \rangle and \langle 0, 1, -1 \rangle\langle 1, 2, 2 \rangle and \langle 3, 3, 0 \rangle\langle 4, -1, 8 \rangle and \langle 2, 2, -1 \rangle\langle 2, -1, 3 \rangle and \langle 1, 5, 1 \rangle
4. The vector u = 27, c, - 67 is a unit vector, and the angle between u and j is acute.
5. A robot arm on a car assembly line carries a bolt in its gripper.
6. A smoothie bar sells small, medium and large smoothies for 4, 5 and 6 dollars.
7. Let v = 2, -6, 3.