Question

Given the vectors OP=(3,4), PQ=(−1,2), and RS=(1,3), determine the vector OQ.

a) OQ=(2,6)
b) OQ=(4,6)
c) OQ=(3,6)
d) OQ=(2,5)

Answer 1

Vector OQ is found by adding the vectors OP and PQ. The resulting components give us OQ=(2,6), making answer choice (a) the correct one.

Step-by-step explanation:

To determine the vector OQ, we need to add the vectors OP and PQ together. This is because vector addition is performed by adding the corresponding components of each vector. The vector OP=(3,4) and the vector PQ=(-1,2). Therefore, to find the vector OQ, we add the x-components and y-components of OP and PQ, respectively:

OQ = OP + PQ = (3 + (-1), 4 + 2) = (3 - 1, 4 + 2) = (2, 6).

This means the correct answer is (a) OQ=(2,6).