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2u2120 section_02.4 /Section 02.4: Problem 8 Previous Problem Problem List Next Problem (2 points) Find two unit vectors orthogonal to a (-1, 2) and b = Enter your ...

Question

2u2120 section_02.4 /Section 02.4: Problem 8 Previous Problem Problem List Next Problem (2 points) Find two unit vectors orthogonal to a (-1, 2) and b = Enter your answer so that the first vector has (1,0,-2) a positive first coordinate First Vector: Second Vector:

2u2120 section_02.4 / Section 02.4: Problem 8 Previous Problem Problem List Next Problem (2 points) Find two unit vectors orthogonal to a (-1, 2) and b = Enter your answer so that the first vector has (1,0,-2) a positive first coordinate First Vector: Second Vector:



Answers

Find two unit vectors orthogonal to the two given vectors. $$\mathbf{a}=\langle 1,0,4\rangle, \mathbf{b}=\langle 1,-4,2\rangle$$

In the way we have the two minute backers to back. And exactly, but off eyes a K tu minus 10103 That is given us minus three. Got minus six. Zia plus Kika still down all toe. Gonna practice. I will be loved minus my last three over Dover off 46 minus six. World overall 46 Once upon a 46. So this is the answer to the problem.

We have the data. That or couple back is a drop off b Will do. I is a k. They want to 10 minus one that is minus to my class. Zika Minus two way have they for two back there is last. My naps minus two would go off one about were off nine and minus. Still wouldn't go out. That is last minus my menstrual country one upon three, minus two upon entry. So this is the answer to the problem.

So in the given question we have two vectors which are given us six J. And minus four. I. And we are told to find the door product and the angle between these victors. So if you are given a victor a one I plus B. One J. And we have to find the daughters of the selector with another victor eight to I plus B two J. We can find it by taking a one times A two plus B, one times B two. So here we we can write the vectors as 09 plus six days because there is no I can handle here. Um It is we have to take the door project with minus four I plus zero J which is Dean, which is which means there is no J component for minus four. I. Right. So when we take the not product we will have zero times minus four. Bless six times 0. Which means this is equal to zero. Right? And now we have found the dot product as zero. So the angle can be found using a formula which says cost it A is equal to aid of be divided by magnitude of a times magnitude of B, where A and B are the two victors. So here we found that the doctor it is equal to zero, right? Which means which means cost data would be equal to zero as well. So now we can write theta is equal to cost inverse of zero, which means we have Theta is equal to 90 degrees. So this is the required answer. That is the dot product of these vectors is zero and the angle between them is 90 leading. So I hope you understood the method. Thank you.

So in the given question we have two vectors which are given us for I minus day and three I minus three. I plus two J. And we are told to find the dark, correct and the angle between these victors. So if a victor ever I I plus B. One J. Is given. And we have to perform the dot product with another victor. A two I I plus B. Two J. We will take the not read of these vectors as even times A two must be one times two. So over here we have four I minus day and the dot product is with minus three I plus two J. Which can be found as four times minus three plus -1 Times two. So this will give us the dark product of the victors as -12 -2, Which is equal to -14. So now that we have the dot product, let's find the angle between these victors. So the angle between these victims can be found using the formula costly to is equal to a dot be divided by magnitude of a times magnitude of B. So the magnitude offers that to you which has given us X way, sorry. Which is given as X. Y plus y. Day can be found using the formula the magnitude of U is equal to square root of x squared plus y squared. So keeping this in mind, we can find the magnitude of four. I blessed day for I minus J. Right so far I minus gate ass the square root of four squared plus negative one squared which is equal to the square root of 16 plus one, which is equal to the square root of 17. And the magnitude of the second with which is my industry, I pressed to j minus three. I plus two. J. Can be found past square root of minus three squared plus two squared which is equal to the square root of nine plus four Which is equal to the square root of 30. So now that we have all the values required to find the angry the angle theater, we can substitute them over here. And we will have negative 14 divided by the square root of 17 times square root of 13. And when we take the value of 14 divided by square root of 17 Times Square Root of 13, We get the value which is equal to negative zero 94942. Right? So now we can take the to is equal to cause in worse off negative -0.942. And when we take the cost universe of negative 0.942, we will get the angle as 1 16.4°.. So this is the required angle in between the given victors. So the Not director of these victors as -14, and the angle between them as 1 60.4°.. So I hope you understood the method. Thank you.


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