Question

Multiplication of a vector by a positive scalar quantity1) changes the direction of the vector, but not the magnitude.2) changes the magnitude of the vector, and the direction.3) changes neither the magnitude of the vector, nor the direction.4) changes the magnitude of the vector, but not the direction.

Answer 1

Multiplying a vector by a positive scalar changes its magnitude but not its direction; therefore, option 4) 'changes the magnitude of the vector, but not the direction' is correct.

Step-by-step explanation:

When a vector A is multiplied by a positive scalar quantity c, the magnitude of the vector changes while the direction remains unchanged. The resulting vector points in the same direction as A. In the context of your question, option 4) 'changes the magnitude of the vector, but not the direction' is correct.

For instance, if vector A represents a displacement of 27.5 meters in a certain direction, and you multiply this vector by a scalar of 3, the resultant vector would represent a displacement of 82.5 meters in the same direction. This exemplifies that only the magnitude of the vector is affected by multiplication with a positive scalar, and it becomes a new vector B, which is parallel to the original vector A: B = αA.

Answer 2

When a positive scaler is multiplied by a vector changes only the magnitude of vector but not the direction of the vector. Therefore, option (4) is correct.