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.

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>

Step 3

F_perpendicular= F - F_parallel

Answer: F_perp...

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