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
 
 Vector:
 PQ + 5RS = (-18, -26)
 Magnitude:
 lPQ + 5RSl = 31.6