Question

Use the dot product to determine whether the vectors are parallel, orthogonal, or neither.v = 2i + 4j, w = 4i + 8j

Answer 1

Answer:

Parallel

Explanation:

Given the vectors:

$\begin{gathered} v=2i+4j \\ w=4i+8j \end{gathered}$

First, find the dot products:

$\begin{gathered} \vec{v}\cdot\vec{w}=(2\times4)+(4\times8) \\ =8+32 \\ =40 \end{gathered}$

The two vectors are not orthogonal because their dot product is not zero.

However:

$\begin{gathered} v=2i+4j \\ w=2(2i+4j) \end{gathered}$

Since they are scalar multiples of each other, the two vectors are parallel.