1. ## Scalar, Vector, Meaningless

State whether the following expressions are vectors, scalars, or meaningless.

I need help with these two.. I think personally, that my answers are right, but perhaps my reasoning is not valid because the back of the book has a diff answer.

Here is what I am thinking:

a) (a x b) + (b x c)
=vector + vector
=scalar
I say the answer is scalar because for example
(4,3,2) + (2,1,2)
=6+4+4
=14<<<< scalar
But the back says vector, what am i missing here?

b) (a x b) - c
=vector - vector
=scalar
I say the answer is scalar because for example
(1,2,3)-(3,2,1)
=-2+0+2
=0<<< scalar
But the back says vector, what did i do wrong here?

c) (a . b) - c
=scalar - vector
=scalar
I say the answer is scalar because for example
4-(4,3,2)
=4(-4,-3,-2)
=-16-12-8
=-36 <<< scalar
what did i do wrong here and what should the answer be?

Note: bolded are vectors

2. Originally Posted by skeske1234
State whether the following expressions are vectors, scalars, or meaningless.

I need help with these two.. I think personally, that my answers are right, but perhaps my reasoning is not valid because the back of the book has a diff answer.

Here is what I am thinking:

a) (a x b) + (b x c)
=vector + vector
=scalar NO it is a vector.
I say the answer is scalar because for example
(4,3,2) + (2,1,2)
=6+4+4
=14<<<< scalar NO it is a vector.
But the back says vector, what am i missing here?

b) (a x b) - c
=vector - vector
=scalar NO it is a vector.
I say the answer is scalar because for example
(1,2,3)-(3,2,1)
=-2+0+2
=0<<< scalar NO it is a vector.
But the back says vector, what did i do wrong here?

c) (a . b) - c
=scalar - vector
=scalar NO it is meanless.
I say the answer is scalar because for example
4-(4,3,2)
=4(-4,-3,-2)
=-16-12-8
=-36 <<< scalar
what did i do wrong here and what should the answer be?

Note: bolded are vectors
The sum or difference of vectors is always a vector.
The cross product of two vectors is a vector.
The dot product of two vectors is a scalar.