A basic understanding of vectors is required for certain concepts in MATH 2015, such as the ideas of directional derivatives and gradient vectors introduced in Section 14.6. If you have trouble with the following questions, please review Sections 12.2-12.3 in the textbook, and the vector summary sheet provided on the course-wide eClass.
Starting at $(x, y) = (1, 1)$, find a unit vector $\mathbf{u} = (a, b)$ that points in the direction of the point $(3, 4)$.
Enter a in the first box, and $b$ in the second. Input example: $a = \sqrt{2}/3$ would be entered into the first answer box as sqrt(2)/3.
$(a, b)$
If $\theta$ is the angle between two vectors $\mathbf{u} = (5, 1)$ and $\mathbf{v} = (3, 2)$, find the value of $\cos(\theta)$.
Input example: $\cos(\theta) = \frac{1}{5\sqrt{3}}$ would be entered into the answer box as 1/(5*sqrt(3)).
Find a unit vector $\mathbf{u} = (a, b)$, where $a$ is negative, that points in the direction perpendicular to the vector $(3, 4)$.
$(a, b)$
