Question

Hello! Would like help on parts b and c. I’m good with A, thanks!

Answer 1

ANSWER:

Part B:

w = 16i + 40j

Part C:

Orthogonal

STEP-BY-STEP EXPLANATION:

Part b

We select a value of c, to determine the value of w, like this:

$\begin{gathered} c=2 \\ \\ w=cv \\ \\ w=2\cdot\left(8i+20j\right) \\ \\ w=16i+40j \end{gathered}$

Part C

We can calculate the relationship between both vectors (t and w) using the dot product, like this:

$\begin{gathered} t\cdot w=\left(-5\right)\left(16\right)+\left(2\right)\left(40\right) \\ \\ t\cdot w=-80+80 \\ \\ t\cdot w=0 \end{gathered}$

When the dot product of two vectors is 0, the vectors form a right angle (90º) with each other. If the dot product of 2 vectors is zero, the vectors are perpendicular, that is, orthogonal.