Question

If P and Q are points in space and we obtain the vector QP and apply a scalar k=-1, what is the new vector?

a) QP
b) PQ
c) -QP
d) -PQ

Answer 1

When a scalar of -1 is applied to vector QP, the result is vector -QP, which is equivalent to vector PQ. Therefore, the new vector is PQ, answer option b).

Step-by-step explanation:

If P and Q are points in space and we obtain the vector QP and apply a scalar k=-1, we essentially reverse the direction of the vector. The new vector will have the same magnitude but opposite direction. Therefore, the new vector is -QP which is equivalent to vector PQ. The correct answer is option b) PQ.

This operation is a standard vector multiplication by a negative scalar which changes the vector's direction while maintaining its magnitude. In vector notation, k multiplied by vector QP would yield kQP, and with k=-1, we have -1*QP, which is simply -QP. Since QP points from Q to P, -QP would naturally point from P to Q, hence PQ.