Question

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

Answer 1

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