Question

Two vectors of lengths 5 and 8 have a dot product equal to -20. Which is true about the vectors?A. The angle between the vectors is acuteB. The angle between the vectors is obtuseC. They point the same direction D. They point opposite directions

Answer 1

B.) The angle between the vectors is

Explanation:

Answer 2

Let's begin by listing out the given information:

Vector 1 = 5

Vector 2 = 8

The dot product is caIculated as shown below:

`\begin{gathered} a\cdot b=|a|*|b|* cos\mleft(\theta\mright) \\ 5\cdot8=|5|*|8|* cos(\theta) \\ \Rightarrow40* cos(\theta)=-20 \\ \Rightarrow cos(\theta)=-(20)/(40) \\ \Rightarrow\theta=\cos ^(-1)(-0.5) \\ \theta=120^(\circ) \end{gathered}`

The angle between the vectors is 120 degrees. Hence, the angle