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Given vector ~v =< 3, 4 > and force vector F~ =< −3, 5 >, finda) The component of F~ parallel to ~v.b) The component of F~ perpendicular to ~v.c) The work, W, done by force F~ through displacement ~v.

Question

Given vector ~v =< 3, 4 > and force vector F~ =< −3, 5 >, find
a) The component of F~ parallel to ~v.

b) The component of F~ perpendicular to ~v.

c) The work, W, done by force F~ through displacement ~v.

check_circleAnswer
Step 1

F~parallel = (F · v) v, where v is a unit vector pointing in the same direction as v.

||v||=sqrt(3^2+4^2)=sqrt(25)=5

unit vector in direction of v=v'=<3/5,4/5>

Step 2

F_parallel= <33/25 , 44/25>

parallel
(F.v)v
기를
-
3 4
3
4
=<-3,5><
5 5
5 5
9
+4
5
3 4
5 5
11 3 4
<
5 5
5
33 44
=<
25 25
help_outline

Image Transcriptionclose

parallel (F.v)v 기를 - 3 4 3 4 =<-3,5>< 5 5 5 5 9 +4 5 3 4 5 5 11 3 4 < 5 5 5 33 44 =< 25 25

fullscreen
Step 3

F_perpendicular= F - F_parallel

Answer: F_perp...

perpendicular
=F-parallel
33 44
=<-3,5>-<
25 25
44
,5-
25
33
=<-3-
>
25
108 81
>
25
=<-
25
help_outline

Image Transcriptionclose

perpendicular =F-parallel 33 44 =<-3,5>-< 25 25 44 ,5- 25 33 =<-3- > 25 108 81 > 25 =<- 25

fullscreen

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