when does vector (a+b) = (a-b)? explain
To find the values of vectors a and b that satisfy the equation (a+b) = (a-b), we can start by expanding the equation using vector addition and subtraction.
Let's assume that vector a = (a1, a2) and vector b = (b1, b2). Now we can substitute these values into the equation:
(a1 + b1, a2 + b2) = (a1 - b1, a2 - b2)
To solve this equation, we need to equate the corresponding components of the vectors:
a1 + b1 = a1 - b1 --> equation 1
a2 + b2 = a2 - b2 --> equation 2
Now let's solve these equations separately:
Equation 1:
a1 + b1 = a1 - b1
By rearranging the terms, we can isolate the variable:
2b1 = 0
Dividing both sides by 2, we get:
b1 = 0
Equation 2:
a2 + b2 = a2 - b2
Again, rearranging the terms and isolating the variable:
2b2 = 0
Dividing both sides by 2, we get:
b2 = 0
So we found that both b1 = 0 and b2 = 0. This means that vector b must be the zero vector (0, 0).
Substituting b1 = 0 and b2 = 0 back into the original equation, we get:
(a1, a2) = (a1 - 0, a2 - 0)
(a1, a2) = (a1, a2)
Therefore, for any values of the components a1 and a2, the equation (a+b) = (a-b) will be satisfied as long as vector b is the zero vector.