Answer:
D. The magnitude is StartRoot 113 EndRoot, and the direction angle is approximately 41°.
Step-by-step explanation:
The correct description of the vector is that the magnitude is √(113) and therefore the direction angle is 41°.
The magnitude of the vector is the length of the vector which can be calculated from the coordinate of its endpoint.
Let (x1,y1) and (x2,y2) are the coordinate of the two endpoints of a vector V.
The magnitude of the vector= |V|= √(y2-y1)²+(x2-x1)²
We have,
Origin of vector = (0,0)
And,
Terminal point = (8, 7)
Here,
a = 8 and b = 7
Now,
To find the magnitude of the vector, we are going to use;
Formula, |v| = √(a² + b² )
|v| = √(8² + 7² )
|v| = √(64 + 49)
|v| = √113
So, the magnitude of the vector is √113.
Now,
Direction angle is find out using ;
Θ = tan ⁻¹ (b / a)
So, Here,
Θ = Angle Direction
Now,
Θ = tan ⁻¹ (7 / 8)
Θ = 41°
Therefore, the proper description of the vector is that the magnitude is √(113) and also the direction angle is 41°.
Learn more about the magnitude of the vector here:
https://brainly.com/question/27708309
#SPJ2
