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Problem 19 Medium Difficulty

Find two unit vectors orthogonal to both $ \langle 3, 2, 1 \rangle $ and $ \langle -1 1, 0 \rangle $.


$$\left\langle-\frac{1}{3 \sqrt{3}},-\frac{1}{3 \sqrt{3}}, \frac{5}{3 \sqrt{3}}\right\rangle,\left\langle\frac{1}{3 \sqrt{3}}, \frac{1}{3 \sqrt{3}},-\frac{5}{3 \sqrt{3}}\right\rangle$$

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Video Transcript

welcome to this lesson in this lesson, we will look for the unit Vector that is also going out to both vectors A and B. Yeah. Okay, so we'll look for actually two unit vectors. If you go now to A and B less than make use of the cross border at that is the determinant of a matrix, starting with I j and K component. Then then this rule as the entries of a mattress. Uh, the vector A. The second part is the increase of the Victor B. Mm. So eight Crosby making good use of the Cooper terminated where we delete the first road. The second column. So you have to one 10 then minus G, we delete the first rule. The second column me after a sorry negative. One 10 Last but not least, is the K part where we delete the first rule in the third column. So we have three negative. One, two, and one. Cool. Mhm. Okay, let's go. Also, a Crosby is equal to I out then two times, everybody's Sarah minus one times one. That is negative. One. Yeah. This area of three times zero that is zero than one times. Okay. One so negative. One times. One. Yeah, that is a positive. Okay, So a positive Because you have negative minus negative. One times. One. It's a positive one. And class K, that is very minus negative. One times two. Okay, so that we have a Cosby given us. Negative. I negative. J don't Glass. Yeah, last five. Okay. Okay, so this is a better. Now we look for the unit vector of this vector, and it's just nothing by the magnitude of vector. So this becomes negative. One to the power to negative one to the bar to again and five to about two. So the mic tattooed, that is one last one last 25. So the whole thing is crude of 27 and that is called Three Square Root of three. Because we have nine times story. Let's call it off. Let's do it that way. You have nine screwed of three. That gives us three screwed of three. Okay, so the union victor you're looking for is a cross be over a cross, be magnitude, and that gives us Yeah. Negative one. Minus negative. G 10 plus five key all over three square root of three. Okay, So the other, the other part is the negative of the whole of this. Yeah, that part was the negative of the whole of that. And that is I Last year, U minus five key all over a tray. Screwed of training all times for a time. This is the end of the lesson. Mhm.