Question

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

Answer 1

Parallel

Step-by-step 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*4)+(4*8) \\ =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.