OUmecheng said:Homework Statement
Consider the three displacement vectors A = ( -2i + 3j ) m, B = ( 2i + 7j ) m, and C = ( -7i + 5j ) m. Use the component method to determine the following.
(a) The magnitude and direction of D = A + B + C
|D| = ___ m
θ = ___° (from the +x axis)
(b) The magnitude and direction of E = -A - B + C
|D| = ___ m
θ = __° (from the +x axis)
The Attempt at a Solution
I don't even know where to begin.
The component method is used to find the magnitude and direction of a vector by breaking it down into its horizontal and vertical components.
The graphical method uses a scale diagram to represent a vector's magnitude and direction, while the component method uses trigonometric functions to calculate the vector's components.
The formula for finding the magnitude of a vector using the component method is M = √(x² + y²), where M is the magnitude, x is the horizontal component, and y is the vertical component.
To find the direction of a vector using the component method, you can use the inverse tangent function (tan⁻¹) to calculate the angle between the vector and the horizontal axis.
Yes, the component method can be extended to three dimensions by breaking the vector down into its x, y, and z components and using the formula M = √(x² + y² + z²) to find the magnitude.