Given that P (5,4), Q=7,3), R = (8,6) and S = (4,1) find the component from of the vector PQ+5RS

Use the information from above to find the magnitude of the vector PQ+5RS

For this case we have the following ordered pairs:

P (5.4)

Q = 7.3)

R = (8.6)

S = (4.1)

For the PQ vector we have:

PQ = Q-P = (7, 3) - (5, 4)

PQ = (2, - 1)

For the RS vector we have:

RS = S-R = (4, 1) - (8, 6)

RS = (-4, - 5)

Then the vector PQ + 5RS is given by:

PQ + 5RS = (2, - 1) + 5 (-4, - 5)

PQ + 5RS = (2, - 1) + (-20, - 25)

PQ + 5RS = (-18, - 26)

Finally, the magnitude of the vector is:

lPQ + 5RSl = root (( - 18) ^ 2 + (-26) ^ 2)

lPQ + 5RSl = 31.6

Answer:

Vector:

PQ + 5RS = (-18, - 26)

Magnitude:

lPQ + 5RSl = 31.6