Final answer:
To determine the x-coordinate of the vector with a given magnitude and direction angles, you use the magnitude (70 lb) and the angle alpha (45 degrees). By calculating x = 70 lb * cos(45 degrees), you find the x-coordinate to be approximately 49.497 lb.
Step-by-step explanation:
To determine the x-coordinate of a vector with a given magnitude and coordinate direction angles, we can use the formula:
x = V * cos(\alpha)
where V is the magnitude of the vector and \alpha is the direction angle with respect to the x-axis.
Given:
- Magnitude (V) = 70 lb
- Alpha (\alpha) = 45°
- Beta (\beta) = 60°
- Gamma (\gamma) = 120°
However, these angles are more likely meant to specify the orientation of the vector in three-dimensional space, which uses the direction cosines to relate the vector components to its magnitude. Assuming the values are correct, we solve for the x-coordinate:
x = 70 lb * cos(45°)
When solving this with a calculator, we get:
x = 49.497 lb (rounded to three decimal places)
This is assuming we're following the standard Cartesian coordinate system where angles are measured from the respective positive axes.