Find the magnitude of -A+B(vectors),where A(vector) = (31.3, 63.9) B(vector) =(88.5, -142.0)
To find the magnitude of the vector -A + B, we first need to calculate the vector -A and then add it to the vector B. Finally, we find the magnitude of the resulting vector.
1. Find -A:
The vector -A is obtained by multiplying each component of A by -1. So, for A = (31.3, 63.9), -A = (-31.3, -63.9).
2. Add -A and B:
To find -A + B, we add the corresponding components of -A and B. So, (-A + B) = (-31.3, -63.9) + (88.5, -142.0) = (88.5 - 31.3, -63.9 - 142.0) = (57.2, -205.9).
3. Calculate the magnitude of (-A + B):
The magnitude of a vector (x, y) can be calculated using the formula √(x² + y²). Applying this formula to (-A + B) = (57.2, -205.9), we get the magnitude:
|(-A + B)| = √((57.2)² + (-205.9)²)
Calculating this expression gives us the magnitude of (-A + B).