Answer:
<3, -1>
3i - j
magnitude = sqrt(10), standard direction angle = -18.4 deg
Explanation:
The end of the arrow is located 3 units to the right and 1 unit down, so it can be represented as <3, -1>
Using i and j for each component of the vector it is also written as
3i - j
Finally, we can write the vector as a magnitude and direction where the magnitude and direction of a vector is
[tex]\begin{gathered} \text{magnitude = }\sqrt[]{x^2+y^2} \\ \text{direction = }\tan ^{-1}(\frac{y}{x}) \end{gathered}[/tex]
So, replacing by (3, -1), we get
[tex]\begin{gathered} \text{magnitude = }\sqrt[]{3^2+1^2}=\sqrt[]{9+1}=\sqrt[]{10} \\ \text{direction = }\tan ^{-1}(-\frac{1}{3})=-18.4 \end{gathered}[/tex]
Therefore, the answers are:
<3, -1>
3i - j
magnitude = sqrt(10), standard direction angle = -18.4 deg
