Question

If v is multiplied by -2.5, the resulting vector’s magnitude is ________, and its angle of direction is ________.

A) 2.5, unchanged
B) 2.5, reversed
C) 6.25, unchanged
D) 6.25, reversed

Answer 1

The resulting vector's magnitude after being multiplied by -2.5 is 2.5 times greater than the original vector, and its direction is reversed, making the correct answer B) 2.5, reversed.

Step-by-step explanation:

The question asks about the effects of multiplying a vector by a negative scalar. When a vector v is multiplied by -2.5, two changes occur. First, the magnitude of the resulting vector is multiplied by the absolute value of the scalar, meaning the magnitude becomes 2.5 times the original magnitude. However, magnitudes of vectors are always positive, so we only consider the absolute value of the scalar. Secondly, the direction of the original vector is reversed, which means the vector points in the opposite direction.

The correct answer to the question is that the resulting vector's magnitude is 2.5 times greater than the original vector's magnitude, and its angle of direction is reversed. Therefore, the correct answer is B) 2.5, reversed.