Given two vectors A = -2i + 3j + 4k and B = 3.00î+1.00ĵ − 3.00k (...

Question

Given two vectors A = -2i + 3j + 4k and B = 3.00î+1.00ĵ − 3.00k (a) find the magnitude of each vector;

Accepted Answer

welcome back everybody. We are given two vectors and we are asked to find the ratio of the magnitude from A to B. So helpful formula here. The magnitude of a given vector is going to be the sum of all their components squared. So the magnitude of say for example given vector A. You're gonna have a X squared plus a Y squared plus A. The squared and the square root of all of that. Now the ratio of the magnitudes from A to B is just going to be equal to the magnitude of a divided by the magnitude of B. So let's go ahead and find those magnitudes. The magnitude of a. Using the above formula is going to be the square root of three squared plus four squared plus five squared. Which when you plug into your calculator gives you five square root two. Now the magnitude for B is equal to the square root of four squared plus two squared plus the square root of five squared. This is equal to five. So then the ratio from A to B. Using this formula above is going to be five square root two divided by five, which is just equal to the square root of two corresponding to our answer choice of a. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one

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