magnitudes and vector length! (1 Viewer)

[Abide]

Hey, does anyone know how to do question such as this one?

If a body is acted on by three forces A, B and C with all lines of action passing through the same point, find the resultant force R, and its magnitude |R| if
A = 3i - 5j + 2k
B = - 2i + 4j + 4k
C = 3i - 3j - 4k

also, how do you determine unit vecotrs again? lol

hmmmmm well, I'm supposed to be helping my little sister get a headstart for the hsc but I really don't have the foggiest, lol

 

[...]

Hey, does anyone know how to do question such as this one?

If a body is acted on by three forces A, B and C with all lines of action passing through the same point, find the resultant force R, and its magnitude |R| if
A = 3i - 5j + 2k
B = - 2i + 4j + 4k
C = 3i - 3j - 4k

also, how do you determine unit vecotrs again? lol

hmmmmm well, I'm supposed to be helping my little sister get a headstart for the hsc but I really don't have the foggiest, lol

dude, vector is not in 3u course

 

[潘偉勤]

I don't recall it being in the 3 unit course either. But...

The resultant force R is the sum of A, B, and C.

R = A + B + C

Basically, what you do is add the coefficients of i, j, and k together like so:

R = (3 - 2 + 3)i + (- 5 + 4 - 3)j + ( 2 + 4 - 4)k = 4i - 4j + 2k

And that is the resultant force.

For magnitudes of vectors, you use this formula.

|R| = (a² + b² + c²)^1/2

|R| = (16 + 16 + 4)^1/2

The magnitude of R, |R| = 6.

Now for unit vectors. If you want to find a unit vector in the same direction as, for example, R then you use this formula.

Ř = R / |R|

Where Ř is the unit vector in the same direction as R (for proper notation, the caron on top of Ř is actually supposed to be a circumflex).

So simply, Ř = 1/6(4i - 4j + 2k) = (2/3, - 2/3, 1/3).

 

[Riviet]

As far as i know, vectors are in the 4 unit course and physics course.

 

[acmilan]

As far as i know, vectors are in the 4 unit course and physics course.

Not those types of vectors though, thats pretty much (in nsw at least) some first year uni stuff.

 

[SeDaTeD]

Yeah, the vecotrs in 4unit and physics are only gone through quite skimpily. Nothing very formal.