Final answer:
The magnitude of the vector with the given components is 10 units and the direction is in the third quadrant, specifically an angle th, between 180° and 270°, where th can be found using the arctangent function, atan2(-6, -8).
Step-by-step explanation:
To find the magnitude A and direction of a vector from its perpendicular components Ax and Ay, relative to the x-axis, we use the Pythagorean theorem for the magnitude and the arctangent function (atan2) for the direction.
Given the x-component is 8 units along the negative x direction, and the y-component is 6 units along the negative y direction, the magnitude can be calculated as:
A = √(8² + 6²) = √(64 + 36) = √100 = 10 units.
The direction of the vector in degrees, called the global angle ϴ (theta), is given by:
ϴ = atan2(-6, -8). Since both components are negative, the vector points in the third quadrant. So, the direction angle ϴ relative to the positive x-axis is between 180° and 270°.