Question

Under what condition A vector + B vector = A vector - B vector

Answer 1

Answer:

A-B and A+B therefore are the two diagonals of this parallelogram. The only way that these “vectors” can be the same, which means both in magnitude and in direction, is in the limit that either A or B is a zero vector.

Step-by-step explanation:

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Answer 2

Answer:

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Step-by-step explanation:

In any vector space, if a+b=a−ba+b=a−b, we can add −a−a to both sides and get b=−bb=−b. Then, adding bb to both sides gives us b+b=0b+b=0.

That is the best we can do. Now, in most vector spaces, b+b=2bb+b=2b, and 2b=02b=0 implies that b=0b=0.

However, that is not true in all vector spaces. For example, the space of polynomials over Z2Z2 has x+x=0x+x=0 for all possible xx, so in that space, two vectors (a+b)(a+b) and (a−b)(a−b) are always equal.