smc-1086-50-Force

A force described by the vector `underset~F = ((3),(6))` newtons is applied to a line `l` which is parallel to the vector `((4),(3))`.

Find the component of the force `underset~F` in the direction of `l`. (2 marks)

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What is the component of the force `underset~F` in the direction perpendicular to the line? (1 mark)

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i. `underset~F = ((3),(6)), \ underset~v = ((4),(3))`

`underset~overset^v = underset~v/(|underset~v|) = underset~v/sqrt(4^2 + 3^2) = 1/5 underset~v=((0.8),(0.6))`

`underset~ F · underset~overset^v`	`= ((3),(6))((0.8),(0.6))`
	`= 3 xx 0.8 + 6 xx 0.6`
	`= 6`

`text(proj)_(underset~v) underset~F`	`= (underset~F · underset~overset^v) underset~overset^v`
	`= 6((0.8),(0.6))`
	`= ((4.8),(3.6))`

ii. `text(Component of)\ underset~F ⊥ l`

`= ((3),(6)) – ((4.8),(3.6))`

`= ((−1.8),(2.4))`