Help with Vectors in R^3 - Noob Question

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Homework Help Overview

The discussion revolves around evaluating expressions involving vectors in R^3, specifically focusing on the definitions and operations of dot products and vector addition. The original poster presents a set of vector expressions and questions their defined status.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore whether to calculate the expressions or simply determine if they are defined. There is a focus on clarifying the meaning of the multiplication symbol used in the expressions, with some indicating it represents a dot product.

Discussion Status

Participants have provided varying interpretations of the expressions, with some confirming the correctness of certain evaluations while others question the definitions of operations involved. There is no explicit consensus on all evaluations, but some guidance has been offered regarding the nature of vector addition and division.

Contextual Notes

There is mention of instructions that may impose constraints on how the expressions should be evaluated, particularly regarding the operations allowed between scalars and vectors.

sibiryk
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First I want to say hello to everyone in here. I'm a noob.

Here is my problem.
Let u=(1.2.0), v=(0,0,3), and w=(0,1,0) are vectors in R^3.
Evaluate, if defined, the following expretions (if undefined state so)

a) (u * v)w
b) u+w*v
c) (u * u)/w
d) (v * v)/(w * w)


Should I try to calculate them or just tell if expretion is defined or undefined?
How can I tell if expretions above are defined?
 
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Should I try to calculate them or just tell if expretion is defined or undefined?

Read the instructions in the question!

Is "*" supposed to represent a dot product, or cross product?
 
James R said:
Read the instructions in the question!

Is "*" supposed to represent a dot product, or cross product?

It is a dot product.
 
"Evaluate" means "calculate."

If you calculate and get a definite answer (a real number or vector) then it is defined.
 
Are my answers correct?

a) 0
b) undefined ( I don't see how I can add scalar to vector)
c) undefined
d) 9
 
a, b, c are correct (you are correct that you can't add a scalar to a vector. In c, division by a vector is not defined). However, in
d) (v * v)/(w * w)
The answer is clearly a fraction.
 
The answer to (d) is correct. It's 9.
 
Hey, 9/1 is a fraction! (blushing)
 

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