SOLUTION: Is my answer correct? Suppose u, v and w are vectors in 3-space. Which are/is defined? A) (v.w) . u B) (w x u) x v My answer is only A is defined

Algebra ->  Matrices-and-determiminant -> SOLUTION: Is my answer correct? Suppose u, v and w are vectors in 3-space. Which are/is defined? A) (v.w) . u B) (w x u) x v My answer is only A is defined       Log On


   

Question 582471: Is my answer correct?
Suppose u, v and w are vectors in 3-space. Which are/is defined?
A) (v.w) . u

B) (w x u) x v

My answer is only A is defined
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A)
This is NOT defined. The expression v.w results to be a scalar. Recall that the dot product a.b is only defined if BOTH a and b are vectors (of the same dimension). But since v.w is a scalar, the dot product isn't defined for z.u where z = v.w (because z is a scalar)

B)
This is defined. Both w and u are vectors in R3. So w x u is a vector in R3. If we let z = w x u, then (w x u) x v becomes z x v. So z is a vector in R3. The quantity v is a vector in R3.

This means that z x v is a vector in R3

Note: keep in mind that the cross product between vectors u and v is only defined if both u and v are vectors in R3 (3-space)