Unit Vectors and I, J Notation Worksheet with Answer Key

What's on the worksheet

1. Write each vector in the other notation (component form to i, j form, or i, j form to component form), and find its magnitude exactly.
   \langle -4, 7 \rangle-\mathbf{i} - 6\mathbf{j}\langle 0, 11 \rangle\sqrt{3}\,\mathbf{i} - \mathbf{j}\langle -2.4, 1 \rangle
2. Find the unit vector in the direction of each vector.
   24\mathbf{i} - 7\mathbf{j}\langle -9, -12 \rangle-\mathbf{i} + 3\mathbf{j}\langle 4, -6 \rangle\langle -\sqrt{5}, 2 \rangle
3. Decide whether each vector is a unit vector.
   -\dfrac{1}{2}\mathbf{i} + \dfrac{\sqrt{3}}{2}\mathbf{j}0.6\mathbf{i} - 0.8\mathbf{j}\dfrac{\sqrt{2}}{2}\mathbf{i} + \dfrac{1}{2}\mathbf{j}-\dfrac{\sqrt{5}}{3}\mathbf{i} - \dfrac{2}{3}\mathbf{j}\dfrac{1}{3}\mathbf{i} - \dfrac{2}{3}\mathbf{j}
4. Write the vector of magnitude L in the direction of w in i, j form, exactly, with no radical in a denominator.
   L = 6, \mathbf{w} = -\mathbf{i} + 2\sqrt{2}\,\mathbf{j}L = 2, \mathbf{w} = 3\mathbf{i} - \mathbf{j}L = 10, \mathbf{w} = \langle -1, -\sqrt{3} \rangleL = 12, \mathbf{w} = -3\mathbf{i} - 3\mathbf{j}
5. The unit vector in the direction of v is 45, - 35, and the j coefficient of v is −6.
6. Ben wants the unit vector in the direction of v = 6i - 8j.
7. Jin is coding a computer game.