14. Use Gram-Schmidt procedure to produce orthogonal vectors from the set of vectorsB =EHHH...

In Problems 15-18, find a scalar a so that the vectors $\mathbf{v}$ and $\mathbf{w}$ are orthogonal. $$ \mathbf{v}=2 a \mathbf{i}+\mathbf{j}-\mathbf{k}, \quad \mathbf{w}=\mathbf{i}-\mathbf{j}+\mathbf{k} $$

No. The question We heard Cuban toe vectors. U N b so that you is, too. I dinos. Uh, she so her in vector the is given as minus dual. I minus she chair. Now we have been asked whether these directors you wouldn't be our or terminal or not. So for two victors you envy to be opened ignored each other off to the order of a no. If your product will always be zero. So he will find off the corporate off given to Victor's who I am minus you'd see. Put up with minus two I minus three chair. So this is equal toe. Uh, do movie pirate minus two. Well, trust nine s aid, Martin. It minus three. The value comes out to the minus 24. That's 24. This is equal to zero. My sense we could also that dog product off you and the sea Quarter. Tzeitel. So therefore you IHS or Dublin Urkal. The oun via pumpernickel. Louisa. So this is our final Confuse him. Thank you

So the question we have been given to Atos you envy such that you is a corrido minus four I and the is a quartile. Sorry is this Plus for I and V is equipped minus I less three j So you can better than us when four I plus zeros here and V is minus, I guess. Cheesier. What will determine whether Director you and Victor v our order vulnerable each other or not before two vectors To be order you know, to each other their daughter brooks would always be zero. So we have to determine the God put up. Lt's to make this first. So you dark v is acquittal for by that's the Sheetal chair door minus I Yes, for you Chair. So this is equal. Ah, four do minus one. That's this. You know in the tree. This is a quartile minus four. That's zero is equal to my nest school. Her sense, you know the door product off you envy is naughty. Border zero in document question. Therefore, we can continue that. Ah, that you and the, uh U nvr north. Not our diviner or not perpendicular to each other. So this is our final conclusion. I'll take you in question. Thank you.

So we have through Victor's given in the question you envy selector you years minus to calm our six on that he is for two. Now we have been asking the question whether the Cuban defectors are doing a lot, not that adept opening locally so that are not so the victims to be or not re center their door must always p zero. So we have to check whether the doctor pay zero or not. Here so broke almost six dork full grammar to then this operation is performed We get the value us minus two they before that's six go to So this is a gurgle minus eight That's doing this is a quarter for no sense. The dog protocol you envy is naughty quarter poor so not equal to zero is a quarter for So therefore you're and the, uh, no perpendicular to each other are not all dignity So had the dog would have been zero, they would have been all doing this. Those artisan Thank you

So for this problem were given unknown vector A and back to be and we're ask defying all vectors a that are with agonal Toby. So what we know then is that x y dot 34 must equal zero. So that means that the re X plus four y equals zero, Which means that why equals minus 3/4 X. So we can say that a must equal some vector such that if we have Alfa for X, then the Y term must be minus 3/4 Alfa and that would be for all, uh, alpha.