Question

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

Answer 1

`^(\to)_(PQ)+4^(\to)_(RS)=<\:-14,-21\:>\:`

`|^(\to)_(PQ)+4^(\to)_(RS)|=7√(13)`

Explanation:

The given points have coordinates; P=(5,4), Q=(7,3), R=(8,6), and S=(4,1).

`^(\to)_(PQ)=^(\to)_(OQ)-^(\to)_(OP)`

`^(\to)_(PQ)=<\:7,3\:>\:-\:<\:5,4\:>`

`^(\to)_(PQ)=<\:7-5,3-4\:>\:`

`^(\to)_(PQ)=<\:2,-1\:>\:`

`^(\to)_(RS)=^(\to)_(OS)-^(\to)_(OR)`

`^(\to)_(RS)=<\:4,1\:>\:-\:<\:8,6\:>`

`^(\to)_(RS)=<\:4-8,1-6\:>\:`

`^(\to)_(RS)=<\:-4,-5\:>\:`

`^(\to)_(PQ)+4^(\to)_(RS)=<\:2,-1\:>\:+4\:<\:-4,-5\:>\:`

`^(\to)_(PQ)+4^(\to)_(RS)=<\:2,-1\:>\:+\:<\:-16,-20\:>\:`

`^(\to)_(PQ)+4^(\to)_(RS)=<\:2-16,-1-20\:>\:`

`^(\to)_(PQ)+4^(\to)_(RS)=<\:-14,-21\:>\:`

The correct answer is C

The magnitude is given by:

`|^(\to)_(PQ)+4^(\to)_(RS)|=√(x^2+y^2)`

`|^(\to)_(PQ)+4^(\to)_(RS)|=√((-14)^2+(-21)^2)`

`|^(\to)_(PQ)+4^(\to)_(RS)|=√(196+441)`

`|^(\to)_(PQ)+4^(\to)_(RS)|=√(637)`

`|^(\to)_(PQ)+4^(\to)_(RS)|=7√(13)`

The correct answer is B