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Let \(\mathbf{u}, \mathbf{v}\) and \(\mathbf{w}\) be vectors satisfying \(\mathbf{u}\bullet \mathbf{v} = 3, \mathbf{u} \bullet \mathbf{w} = 4, \mathbf{v} \bullet \mathbf{w} = 5.\)

 

Then what are \((\mathbf{u} + 2 \mathbf{v})\bullet \mathbf{w}, (\mathbf{w} - \mathbf{u})\bullet \mathbf{v}, (3\mathbf{v} - 2 \mathbf{w})\bullet \mathbf{u}\)equal to? Enter the list in the order above.

 Apr 30, 2020
 #1
avatar+468 
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Try the method of substitution. You can put every variable in terms of another variable. For example, you could write u as 3/v, and w as 5/v. Where does that get you?

 Apr 30, 2020
 #2
avatar+111435 
+2

Here's my best attempt

 

(u +2v) * w  =  uw  + 2vw   =  4 + 2(5)  =  14

 

(w - u) * v  =   wv  - uv  =   5 - 3   =  2

 

(3v - 2w) * u   =     3vu - 2uw  =  3(3)  - 2(4) =  9 - 8   =  1

 

cool cool cool

 Apr 30, 2020

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