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Find the angle between Ihe given vectors. Rourid lo Ihe nearost tonth of degree_u=6i - 3j,v =4i0 A. 12 4" 0 B. 34,8" C C; 2 40 24 89...

Question

Find the angle between Ihe given vectors. Rourid lo Ihe nearost tonth of degree_u=6i - 3j,v =4i0 A. 12 4" 0 B. 34,8" C C; 2 40 24 89

Find the angle between Ihe given vectors. Rourid lo Ihe nearost tonth of degree_ u=6i - 3j,v =4i 0 A. 12 4" 0 B. 34,8" C C; 2 40 24 89



Answers

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)
$$
\mathbf{a}=\langle- 1,3,4\rangle, \quad \mathbf{b}=\langle 5,2,1\rangle
$$

In this question we are going to find the angle between two vectors. The formula is on the screen, we start with the dot product in the numerator. For product we multiply negative four times eight Plus one times -2. And we need the magnitudes in the denominator magnitude of the first vector is square root of negative four squared plus one squared. Yeah. And the magnitude of the second vector is square root of eight squared Plus -2 Squared. And then with our calculator in degree mode we will find inverse co sign of -34 divided by Square root of 17 times 68. Mhm. So in verse co sign negative 34 divided by the square root of 11 56. Mhm. That is an angle of 180°.

The question was given a better i e go do two is money to be Could do the the minus 20 for here And for we can find the land on the I You could get a square under juice square Bless no square Blessed managed to square Then we can equals you that you square in the to and father be we get the same thing and we get equal to the square under iso square Blessed honest your square less for square And then you get a coach in the square it on the 20 And then we get equal to that juice Colonel of five and no, we want to find Ah, I goes I angle determined village inventors And we caught you. They knew I don't be over the no under a times the norm, Toby, And just be here. We're ICO Judah Two times air blood The temps Manus, Jew Minister Times far be writing by juice with the Jew tense juice curled up five. And then we get echo to the minus eight over the for squared under 10. Then we get to go to no minus do off a skirt 10 and from here, we get the Anglo Teton. We could, you know. Of course. I involves under monster and top square it under 10. Here. Yeah, we get it. Ah, Minus Judy. Very misguided. Under 10 goes. I am president. And so I go to is around 129 on gentle training.

The question is asking about the angle between the given direct us to the nearest tent over degree and directors are is it was too minus three minus three and basic was too minus fight. Now the thing the angle which we are going to find out is Host Tita is it was toe? Hey, don't be divided by more off. Pay more off Be so a Don't be so don't productive A and B is minus three multiplied by minus fight which is 15 only and minus three multiplied by two with his minus six divided by more off eight which is please quiet minus three square tradition off these minus three squares. So nine plus nine, which is 18 then again multiplied by Squire group off minus minus five is 25 to describe it is four so 29. So this ISS 15 minus six is nine. Derided by Quirot 0 18 multiplied by 29. So close Tita, is it close to 1900 by Esquire Rudolph 18 multiplied by 29 so we can write it as nine Divided by three Esquire. Rude Oh, rumor deployed by 20 night. So this is this now finally t tight equals toe cause in new worse off three divided by Squire route off humor deployed by 20 night, which is 58. So this is the coast in worse for the teeter And finally, that he does you will be 66.0 degree And if you want to write this to the nearest pent, which is 70 bigotry So this is the complete answer for this question.

To find the angle between these two vectors. We're gonna want to make use of the two definitions of dot product. So what is the dot product? We know there's two definitions, there's the magnitude of eight times the magnitude to be times coastline data. And then there's also the some A one B. One, the sum the product of the some. So A one, B. One plus a two B. Two and possibly more than that. So in this case we want to use both. So using this definition we end up getting eight minus three which is five. So that's the dot product. 8 -3, Yep, That's five. And then using the other method we get the magnitude of A is going to be five. The magnitude of B is route five. So then this is cosign theta. So then what we do is we divide and we get one over root five equals cosign data, which means data equals the inverse co sign Of One Over Root five. When we do that, we end up getting a final answer of theta Equalling 63°


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