What is the value received by multiplying a’s magnitude by b’s magnitude and the sine of the angle between them?

The value obtained by multiplying the magnitude of vector a by the magnitude of vector b and the sine of the angle between them is known as the magnitude of the resultant vector when the two vectors are combined in such a way that their directions are considered. This concept arises from the analysis of vector cross products or in determining the area of the parallelogram formed by the two vectors.

In vector mathematics, the formula for the magnitude of the resultant vector formed by two vectors includes the sine of the angle to account for the directional component of the vectors. This relationship shows the effect of the angle on how the two vectors interact with each other when combined.

The other options refer specifically to the magnitudes of the individual vectors or suggest that an alternative fixed value is derived from the multiplication, which does not align with the concept of vector addition or the geometric implications of vectors in a plane. Therefore, the correct answer accurately reflects the mathematical relationship governing the combination of the two vectors when taken into account their magnitudes and the sine of the angle between their directions.