P, Q, R, S are points in a plane such that PQ = 8i - 5j, QR = 5i + 7j, RS = 7i + 3j and PS = xi + yj. Find (x, y).
Answer Details
Given that PQ = 8i - 5j, QR = 5i + 7j, RS = 7i + 3j, and PS = xi + yj.
Since PQ + QR + RS = PS, we have:
(8i - 5j) + (5i + 7j) + (7i + 3j) = xi + yj
Simplifying the left-hand side, we get:
20i + 5j = xi + yj
Equating the corresponding components, we have:
20 = x and 5 = y
Therefore, the coordinates of point S are (20, 5).
Hence, the correct answer is (20, 5).