I cant seem to get the right answer, it's like I'm missing something. Can someone please help? Thanks.
I cant seem to get the right answer . Find a unit vector that is orthogonal to both $u$ and $v$, $u=(-8,-6,4)$, $v=(10,-12,-2)$
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calculus
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2Take the cross product – 2017-01-29
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0I did but still can't – 2017-01-29
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0Convert it to a unit vector by finding the norm.. – 2017-01-29
3 Answers
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Hint
$$w=u\times v$$
Is a vector orthogonal to both, $u$ and $v$.
So, you are looking for
$$\frac{w}{|w|}$$
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$$(-8,-6,4)\times (10,-12,-2)=\begin{vmatrix}i&j&k\\-8&-6&4\\10&-12&-2\end{vmatrix}=(60,24,156)=12(5,2,13)$$
and now just evaluate $\;\left\|(60,24,156)\right\|=12\sqrt{25+4+169}\;$ and ...
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Take the cross product of $u$ and $v$; this produces a vector, almost certainly not of unit length. You then need to find a unit vector pointing in the same direction.
Given a vector (for example, $(1, 2, 3)$), to obtain the unit vector in the same direction, you just need to divide by the length. In the case of $(1, 2, 3)$, the length is $\sqrt{14}$, so the unit vector is $(\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}})$.