Physics · Scalars and Vectors
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The difference of a vector B and its negative vector –B is:
- A
A null vector
- B
Equal to magnitude of vector B
- C
Twice the magnitude of vector B
- D
Smaller than magnitude of vector B
Option C is correct. The difference between vector B and its negative vector -B is equivalent to B - (-B), which simplifies to B + B = 2B. Thus, the magnitude of the resulting vector is twice that of vector B.
Option A is incorrect because a null vector occurs when two opposite vectors are added, not subtracted.
Option B is incorrect because the magnitude of the difference between a vector and its negative cannot equal the magnitude of the original vector.
Option D is incorrect because the magnitude of the resulting vector from B - (-B) will be larger, not smaller, than the magnitude of vector B.
A null vector results from the sum of two opposite vectors, not their difference.
The magnitude of the difference cannot be equal to the magnitude of one of the vectors involved in subtraction when the vectors are opposite.
The difference between a vector and its negative is equivalent to adding the two, resulting in a vector with twice the magnitude of the original.
The magnitude of the difference will be greater, not smaller, since the vectors add up.
Tagged under Physics · Scalars and Vectors · 2010