The vector (3, 1) represents a displacement or a directed line segment in two-dimensional space. To find the magnitude and angle of this vector, we can use trigonometry.
1. Magnitude: The magnitude of a vector represents its length or size. We can find the magnitude of a vector using the Pythagorean theorem. For the vector (3, 1), the magnitude can be calculated as follows:
magnitude = sqrt((3^2) + (1^2)) = sqrt(9 + 1) = sqrt(10) ≈ 3.16
Therefore, the magnitude of the vector (3, 1) is approximately 3.16.
2. Angle: The angle of a vector represents the direction in which it is pointing. We can find the angle of a vector using trigonometry. For the vector (3, 1), the angle can be calculated as follows:
angle = arctan(1/3) ≈ 0.321 radians ≈ 18.43 degrees
Therefore, the angle of the vector (3, 1) is approximately 0.321 radians or 18.43 degrees.
So, the magnitude of the vector (3, 1) is approximately 3.16 and the angle is approximately 0.321 radians or 18.43 degrees