# Vector Assignment 2

Problem 1.  Compute the magnitude of the vector $\vec{v} = \langle \, 1, 2, 3, 4, 5 \, \rangle$ and compute the magnitude of the vector $\vec{v} - 2\vec{w}$ where $\vec{w} = \langle \, 1/2, 3, 0, 2, -1 \, \rangle$.

Problem 2.  (a) Draw a picture of the vector $\vec{v} = \langle\, 1, 2 \, \rangle$ in standard position in $\mathbb{R}^2$.

(b) Find all numbers $c \in \mathbb{R}$ so that $\vec{v}$ (from part (a) above) is perpendicular to the vector $\vec{w} = \langle \, 1, c \rangle$.  Once you have found all possible values for $c$, pick one and draw the vector $\vec{w}$ in the same picture you from part (a) where you drew the vector $\vec{v}$.

Problem 3. (a)   Draw a picture of the set of points $S \subset \mathbb{R}^2$ defined by

$\displaystyle S = \left \{ (x,y) : x^2-2x + y^2 = 8 \right\}.$

(b) Draw a picture of the set of points $S \subset \mathbb{R}^3$ defined by

$\displaystyle S = \left \{ (x, y, z) : x^2 - 4x + y^2 - 2y + z^2 = -4 \right\}.$

Problem 4.  Complete the definition of the dot product between two vectors $\vec{v}, \vec{w} \in \mathbb{R}^n$ where $\vec{v} = \langle \, v_1, v_2, \cdots, v_n \, \rangle$ and $\vec{w} = \langle \, w_1, w_2, \cdots, w_n \, \rangle$:

$\displaystyle \vec{v}\cdot \vec{w} =$

Problem 5.  Exercise 1 from Section 9.3 of our textbook.

Problem 6.  Exercise 3 from Section 9.3 of our textbook.