If A B, under what condition is | -
| = A - B?
A) The statement is never true.
B) Vectors and are in opposite directions.
C) Vectors and are in the same direction.
D) Vectors and re in perpendicular directions.
E) The statement is always true.

Question

If A > B, under what condition is |  - 
| = A - B?
A) The statement is never true. 
B) Vectors and are in opposite directions. 
C) Vectors and are in the same direction. 
D) Vectors and re in perpendicular directions. 
E) The statement is always true.

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 |