If A B, under what condition is | -
| = A - B?

Question

If A > B, under what condition is |  - 
| = A - B?

Quizplus · Accepted Answer

The given expression can be written in vector form as |u - v|, where u and v are the given vectors. Using the triangle inequality, we have:

|u - v| ≤ |u| + |v|

Since |u| = A and |v| = B, and A > B, we have:

|u - v| ≤ A + B

Therefore, if |u - v| = A - B, we must have A + B = 0, which is not possible since A and B are both non-negative. Thus, the statement can never be true.

However, if vectors 11eab6cc_1d81_7b32_a957_3531fd827353_TB4469_00 and 11eab6cc_1d81_7b33_a957_7f3285e4076d_TB4469_00 are in the same direction, then u - v is a scalar multiple of one of the vectors, and we have:

|u - v| = |k(u - v)| = k|u - v| = k|u| - k|v|

If we choose k = 1/(A+B), then k|u| - k|v| = A - B, and the statement is true. Therefore, the best choice is C.

If a > B, Under What Condition Is |