1. ## vector calculus

for each expression, determine whether or not it makes sense..explain

a*(b*c) ..the back of the book says this doesn't make sense but i don't know why..

2. you can aonly take the dot product of a vector with a vector

a*(b*c)

b*c is a scalar (number)

so you can't take the dot product of the vector a with a nunber

3. thanks so its the same thing with
(a*b)/c then? because a*b is a number

4. no --- iit makes no sense because you can't divide by a vector-- there is no such operation.

if c were a constant(a*b)/c is just a number over a number which would makes sense

5. ohh okay..so my last one is
(the magnitude of a)^2 * b - (a*b)^2 *a

6. Same reason as the first

(the magnitude of a)^2 * b - (a*b)^2 *a

(the magnitude of a)^2 is a scalar

(a*b)^2 is a scalar

again you can't take the dot product of a scalar and a vector

7. the back of the book says its right though..hmm. oh well. thank you for all of your help with everything!! youre the best

8. you can take a scalar times a vector but not the dot product of a scalar

with a vector

so if the question was (|a|^2)b without the dot it makes sense

Similarly[(a*b)^2]a would make sense if you are not talking about the dot product

9. thank you!