Write each vector in the form 〈a, b〉. Write answers using exac...

Question

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

Accepted Answer

Welcome back. I am so glad you're here. We are told a vector is shown in the figure, write it in the form A B express your answers as exact values or round them to four decimal places. If necessary, then we're given a figure with a vertical Y axis and a horizontal X axis. They come together at the origin in the middle. Then we have a position vector on there, meaning its initial point is at the origin and it extends down into the fourth quadrant. Its measure is negative 50 degrees and its magnitude is labeled 19 and it's labeled as vector V. Our answer choices are answer choice A nine square root three divided by two comma negative 11 square root two divided by three answer choice B seven square root two divided by two comma negative eight square root five divided by three answer choice C 11.0987 comma negative 13.0994. And answer choice D 12.2130 comma negative 14.5548. All right. So we are writing our vector in the format of U equals A comma B but we're told here that our vector is labeled V. So it's going to end up being V equals. Now, we just have to figure out what A and B are. And we recall from previous lessons that A is going to be the horizontal component. And we find that by taking our magnitude of our vector, so the magnitude of U multiplied by the cosine of theta and B is our vertical component. We find that by taking the magnitude of our vector U and multiplying that by the sign of theta. So what's our magnitude of our angle? And what's our theta? Well, we could see from the figure that our magnitude of our vector V is equal to. We recall that that's the length of our vector and it's labeled as 19 and our theta is going to be a negative 50 degrees. So solving for a, that would be our magnitude is 19 multiplied by the cosine of theta is negative 50 oops, I'm writing 15 but saying 50 it's negative 55 0 degrees. And for B for the vertical component, that's going to be again, the magnitude is 19 multiplied by the sign of the same theta, negative 50 degrees. So now it's just plugging that into a calculator, make sure when you plug it into your calculator, it's in degrees mode. And for a, for the horizontal component, you'll get something like 12.21296 that'll keep going. And for B for the vertical component that's going to be something like negative 14.55484. And that keeps going. But rounding to four decimal places for, for the A, the fourth decimal places in nine looks to the six and rounds up. So that one will be 12.2130. And for the B the fourth decimal places an eight, it looks to the four and remains an eight. So that one is negative 14.5548. And there we have, oops, that's not the highlighter. There we have our A comma B, we look at our answer choices and that matches with answer choice. D well done. We'll catch you on the next one.

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

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Key Concepts

Vectors

Coordinate System

Exact Values vs. Decimal Approximations

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