Question

Given that p(5,4), q=(7,3), r=(8,6) and s=(4,1) find the component from of the vector pq+3rs

Answer 1

The vector pq is given by:
pq = q - p = (7.3) - (5.4)
pq = (7-5, 3-4)
pq = (2, -1)
The vector rs is given by:
rs = s - r = (4,1) - (8.6)
rs = (4-8, 1-6)
rs = (-4, -5)
Then, the vector pq + 3rs is given by:
pq + 3rs = (2, -1) + 3 (-4, -5)
pq + 3rs = (2, -1) + (-12, -15)
pq + 3rs = (2-12, -1-15)
pq + 3rs = (-10, -16)
Answer:
The component from the vector pq + 3rs is:
pq + 3rs = (-10, -16)