(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the component of the force [tex]\vec{F} = 2\hat{i} - 2\hat{j} + \hat{k}[/tex] in:

a) the direction [tex](\hat{i} + \hat{j} - \hat{k})/\sqrt{3}[/tex]

b) the direction of the vector [tex]3\hat{i} + 2\hat{j} - 6\hat{k}[/tex]

2. Relevant equations

[tex]dir \vec{A} = \vec{A}/|\vec{A}|[/tex]

3. The attempt at a solution

a) I broke [tex]\vec{F}[/tex] down into components [tex]<2\hat{i}, 2\hat{j}, \hat{k}>[/tex]. Then I figured that F goes [tex]2\hat{i}[/tex] in direction [tex]i[/tex], goes [tex]-2\hat{j}[/tex] in direction [tex]j[/tex], then goes [tex]-\hat{k}[/tex] in direction [tex]k[/tex], giving an overall Force component of [tex]<2\hat{i}, -2\hat{j}, -\hat{k}>[/tex].

b) I did the same thing and since the signs in each direction were the same as in a), I ended up with the same answer: [tex]<2\hat{i}, -2\hat{j}, -\hat{k}>[/tex].

It seems to make sense, but I am pretty uncertain, so I thought I would ask here.

Thanks!

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# Homework Help: Vector and Force Components

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