Given two vectors, a and b, such that a + b = a - b, find the magnitude of b.
Consider the equation
a + b = a - b
to be n vector notation and both a and b have components. Subtract the a vector from both sides. You are left with
b = -b
That can only be true if b = 0. That would make its magnitude also zero.
To find the magnitude of vector b when a + b = a - b, we can rewrite the equation as:
a + b = a - b
Subtracting vector a from both sides, we have:
b = -b
This equation tells us that vector b is equal to its negation, which means that the magnitude of vector b must be zero.
Therefore, the magnitude of vector b is 0.