Solving for Vector Multiplication: 4.00C · (3.00 A × B) Explained

[mossfan563]

For the following three vectors, what is 4.00C ·(3.00 A × B)?

I'm confused. How do I approach this problem with coefficients?

 

[swooshfactory]

you probably need to take the square of, in A for instance, 2^2 + 3^2 + (-4)^2, which would give you the magnitude for A which here I think is referred to as A. do the same for C and B (square the coefficients before i, j, and k, take the square root and treat the answers as B and C, respectively. then use those answers as the variables in the equation in the beginning and you should have an answer.

 

[mossfan563]

The A that I put in 4.00C ·(3.00 A × B)? is really the vector symbol. Not just regular ol' A in AB cos(theta).

Should I still do that anyways?

 

[jackiefrost]

Try specifying your vectors in component form.

For example:

A = a1*i + a2*j + a3*k
B = ...
C = ...

Start with the simple scalars. What's 4*C in component form? 3*A?

Then take the cross product and express the resultant vector also in component form. Then do the dot product.

Can you see why I used three components for A instead of only two? [Hint: what's the direction of the resultant vector of the cross product?]

jf

 

[HallsofIvy]

you probably need to take the square of, in A for instance, 2^2 + 3^2 + (-4)^2, which would give you the magnitude for A which here I think is referred to as A. do the same for C and B (square the coefficients before i, j, and k, take the square root and treat the answers as B and C, respectively. then use those answers as the variables in the equation in the beginning and you should have an answer.

No, there is no reference to the magnitude of vectors here. "x" represents the cross product of two vectors and "." represents the dot product of two vectors.

 

[mossfan563]

I know how to do cross products and dot products.

But for 4C do i multiply 4 times C and the result of (3 A X B)? or Do I just multiply 4 C? and it has no k value. How does that factor? Is that 0 k?

 

[mossfan563]

Anyone?

 

[swooshfactory]

disregard my advice...i think i was wrong.

 

[tiny-tim]

I know how to do cross products and dot products.

But for 4C do i multiply 4 times C and the result of (3 A X B)? or Do I just multiply 4 C?

Hi mossfan563!

I would leave the 4 until the end … less chance of my making a mistake!

and it has no k value. How does that factor? Is that 0 k?

Yup!