Which Operations Are Valid for Vectors and Scalars?

[vorcil]

groups: Vectors / Scalars / doesn't make sense
Which of these groups do the following belong too

1: a.b + b.c
2: a+(a.b)
3: (b.b)b+a
4: (a.b)(b.c)
5: (a.b).c

a.b + b.c is adding the dot product of two vectors, then adding them so a Scalar for the final

a+(a.b) is adding a vector to a product of two vectors so doesn't make sense e.g (1,1,1)+5

(b.b)b+a also doesn't make sense, since it is the dot product of a vector added with two added vectors e.g (b*b=5)*(2,1,0)+(1,1,1)

(a.b)(b.c) makes sense, and is a scalar, because the two dot products produce scalars which are then multiplied by each other

(a.b).c is a vector because you get a scalar from a.b then multiply each component of C to create a new vector

-

hoping someone could check for me XD thanks

 

[vorcil]

really not sure about

(b.b)*(a+b)

i know a*(b+c) works
but (b.b)is a scalar not a vector so can't be the same as
(b.b)*b + (b.b)*c

could someone please clarify

 

[vorcil]

3: (b.b)(b+a)
is the same as
5: (a.b).c

scalar multiplied by a vector = vector

 

[vorcil]

lol what a stupid thread, wish I hadn't made it

- suppose i could've done the same thing on paper

 

[Mark44]

I'm not sure what you concluded for 3 and 5.
In your first post you have
3) (b.b)b + a
and then later you have (b.b)(b + a)
b.b is a scalar
(b.b)b is a scalar times a vector (= a vector)
(b.b)b + a is a vector + a vector, which is a vector.

(b.b)(b + a) is also a vector, but a different one from (b.b)b + a.

5) (a.b).c is not a vector. This is a scalar dotted with a vector, which is not defined. The dot product is defined only for two vectors.

 

[vorcil]

5) (a.b).c is not a vector. This is a scalar dotted with a vector, which is not defined. The dot product is defined only for two vectors.[/QUOTE]

But when you get the Scalar a.b, then multiply the vector c by the scalar don't you get a vector?

e.g

a=(2,2,2) b = (3,3,3) c = (4,4,4)

(a.b).c
a.b = 6 + 6 + 6 = 18

then 18 * c
18(4,4,4)
=(18*4,18*4,18*4)
=(72,72,72)
isn't that the result when you multiply a scalar be a vector?

 

[Mark44]

5) (a.b).c is not a vector. This is a scalar dotted with a vector, which is not defined. The dot product is defined only for two vectors.

But when you get the Scalar a.b, then multiply the vector c by the scalar don't you get a vector?
[/quote]
You are confusing scalar multiplication with the dot product. I am assuming that the periods you used in (a.b).c mean "dot product." In that case you have a scalar dotted with a vector, which is undefined.

If, on the other hand, you had written (a.b)c (without the second period), then the multiplication would be scalar multiplication, which is defined for a scalar and a vector.

e.g

a=(2,2,2) b = (3,3,3) c = (4,4,4)

(a.b).c
a.b = 6 + 6 + 6 = 18

then 18 * c

No, it would be 18 . c, not 18 * c. This is where you are confusing the dot product with scalar multiplication.

Dot product
Inputs: two vectors
Output: a scalar

Scalar multiplication
Inputs: a scalar and a vector
Output: a vector

Hope that's clear.

18(4,4,4)
=(18*4,18*4,18*4)
=(72,72,72)
isn't that the result when you multiply a scalar be a vector?