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

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)