Magnitude and Direction of a Vector Worksheet with Answer Key

What's on the worksheet

1. Find the magnitude of each vector exactly.
   \langle -12, 35 \rangle\langle 6, -3 \rangle\langle -1.5, 2 \rangle\langle 2\sqrt{2}, -1 \rangle\left\langle \dfrac{5}{13}, -\dfrac{12}{13} \right\rangle
2. Find the magnitude of each vector exactly, and its direction angle in degrees, exactly or to the nearest tenth of a degree.
   \langle -4\sqrt{3}, 4 \rangle\langle -2, -2 \rangle\langle 6, -1 \rangle\langle -8, 3 \rangle\langle 0, 7 \rangle
3. Write each vector in component form, exactly where the angle allows, otherwise to the nearest hundredth.
   \|\mathbf{v}\| = 10, \theta = 135^\circ\|\mathbf{v}\| = 6, \theta = 330^\circ\|\mathbf{v}\| = 20, \theta = \dfrac{4\pi}{3}\|\mathbf{v}\| = 7, \theta = 180^\circ\|\mathbf{v}\| = 25, \theta = 112^\circ
4. Arjun drives a remote-control car across a school gym floor marked in meters, with x east and y north.
5. The vector from A(2, -1) to B(x, 10) has magnitude 61.
6. A vector v has magnitude 58.