I don't know how to approach this problem. I tried a few things but didn't get anywhere.

X

Let U,V & W be 3 vectors,which of the following make sense and which does not?
1) ( U x V ) . W
2) U x ( V.W )
3) U x ( v x W)
4) U. ( V . W )

Relevant page
<a href="/vectors/vectors-intro.php">Introduction to Vectors</a>
What I've done so far
I don't know how to approach this problem. I tried a few things but didn't get anywhere.

My best suggestion is to just create some different vectors and some angles between them, and then try to calculate each of those expressions. Some will work and some will not.

Plug in any numbers you like into the vectors and then find the value of each expression.

Show your working so that I can spot where you are having trouble. I encourage you to use the math input system so your math is easy to read.

X

My best suggestion is to just create some different vectors and some angles between them, and then try to calculate each of those expressions. Some will work and some will not.
Plug in any numbers you like into the vectors and then find the value of each expression.
Show your working so that I can spot where you are having trouble. I encourage you to use the math input system so your math is easy to read.

`U = 4` pointing to `0°`, `V = 6` acting at `40°` to `U`, and then `W = 5` at `30°` to `V`.

1) `(U xx V) \cdot W` ` = (4 xx 6 sin 40° "n") \cdot V`

`= 15.43 "n" \cdot V`

`= 15.43 xx 5 xx cos 30°`

`= 66.8`

I get an answer so I guess this one "makes sense".

Am I on the right track?

X

I'll try
`U = 4` pointing to `0°`, `V = 6` acting at `40°` to `U`, and then `W = 5` at `30°` to `V`.
1) `(U xx V) \cdot W` ` = (4 xx 6 sin 40° "n") \cdot V`
`= 15.43 "n" \cdot V`
`= 15.43 xx 5 xx cos 30°`
`= 66.8`
I get an answer so I guess this one "makes sense".
Am I on the right track?

2) `U xx ( V \cdot W )` ` = U xx (6 xx 5 xx cos 30°)`

`= U xx 25.98`

But you can only do cross multiply with 2 vectors. So this one doesn't make sense.

I think I'm getting it now.

3) `U xx ( V xx W)` ` = U xx (6 xx 5 xx sin 30°"n")` ` = U xx 15"n"`

`= 4 xx 15 xx sin(90°)`

`=60`

4) `U \cdot ( V \cdot W )` ` = U \cdot (6 xx 5 xx cos(30°)`

`= U \cdot (25.98)`

Once again, we can't do dot product of a vector and a scalar,

So the first and 3rd ones have meaning, while the 2nd and 4th do not.

X

OK, thanks.
2) `U xx ( V \cdot W )` ` = U xx (6 xx 5 xx cos 30°)`
`= U xx 25.98`
But you can only do cross multiply with 2 vectors. So this one doesn't make sense.
I think I'm getting it now.
3) `U xx ( V xx W)` ` = U xx (6 xx 5 xx sin 30°"n")` ` = U xx 15"n"`
`= 4 xx 15 xx sin(90°)`
`=60`
4) `U \cdot ( V \cdot W )` ` = U \cdot (6 xx 5 xx cos(30°)`
`= U \cdot (25.98)`
Once again, we can't do dot product of a vector and a scalar,
So the first and 3rd ones have meaning, while the 2nd and 4th do not.