Part A
given that P=(5,4), Q=(7,3), R=(8,6), and S=(4,1), find the component form of the vector PQ+4RS.
a.(18,19)
b.(-2,-6)
c.(-14,-21)
d.(-18,-19)
Part B
Use the information from part A to find the magnitude of the vector PQ+4RS.
a. 2sqrt10
b. 7sqrt13
c. sqrt35
d. 637
P=(5,4), Q=(7,3), R=(8,6), and S=(4,1), find the component form of the vector PQ+4RS
To get you started,
PQ = Q-P = (7-5,3-4) = (2,-1)
RS = S-R = (4-8,1-6) = (-4,-5)
So, PQ+4RS = (2,-1)+4(-4,-5) = ...
Using the info. oobleck gave, the answer would be C because 4(-4,-5) is just (-16,-20), and that plus (2,-1) is (-16 + 2, -20-1), which is just (-14,-21) in turn.
Using the information oobleck gave, the answer would be C because 4(-4,-5) is just (-16,-20), and that plus (2,-1) is (-16 + 2, -20-1), which is just (-14,-21) in turn.
Using the info. oobleck gave, the answer would be C because 4(-4,-5) is just (-16,-20), and that plus (2,-1) is (-16 + 2, -20-1), which in turn is just (-14,-21).
Using the information oobleck gave, the answer would be C because 4(-4,-5) is just (-16,-20), and that plus (2,-1) is (-16 + 2, -20-1), which in turn is just (-14,-21).
Part A:
To find the component form of the vector PQ+4RS, we first need to find the component form of vector PQ and vector RS.
Vector PQ:
To find the component form of vector PQ, we subtract the coordinates of point P from the coordinates of point Q.
PQ = (Qx - Px, Qy - Py)
= (7 - 5, 3 - 4)
= (2, -1)
Vector RS:
To find the component form of vector RS, we subtract the coordinates of point R from the coordinates of point S.
RS = (Sx - Rx, Sy - Ry)
= (4 - 8, 1 - 6)
= (-4, -5)
Now that we have the component form of vector PQ and vector RS, we can find the component form of PQ+4RS by adding the respective components together.
PQ+4RS = (PQx + 4RSx, PQy + 4RSy)
= (2 + 4(-4), -1 + 4(-5))
= (2 - 16, -1 - 20)
= (-14, -21)
So, the component form of the vector PQ+4RS is (-14, -21).
Therefore, the correct answer to Part A is c. (-14, -21).
Part B:
To find the magnitude of the vector PQ+4RS, we can use the formula for the magnitude of a vector:
Magnitude = sqrt((Px + Qx)^2 + (Py + Qy)^2)
Substituting the component form of PQ+4RS into the formula:
Magnitude = sqrt((-14)^2 + (-21)^2)
= sqrt(196 + 441)
= sqrt(637)
So, the magnitude of the vector PQ+4RS is sqrt(637).
Therefore, the correct answer to Part B is d. 637.
I don't see your choices.
How can I check your answers?