In Exercises 47–52, write the vector v in terms of i and j whose ...

Question

In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given.

||v|| = 12, θ = 225°

Accepted Answer

Or a vector V with the following magnitude in angle Q in the grease express it in terms of I and J. But we have the magnitude of V is equals to 16 and Q equals 315 degrees. We have four possible answers. All vectors in the form of I and J. Let's see if we can solve this problem. First, we know the standard form of the vector is given by the V equals X I plus Y J. This means we need to solve for the X and Y components and a vector. Our opponent as given by the magnitude of V multiplied by cosine of the angle Q for the Y is the magnitude of V multiplied by a sign of the angle Q. So for X, we will get 16 cosine of 315 degrees or a why we will get 16th sine of degrees. Now, based on the unit circle coast side at 315 degrees is the square root of two divided by two, which means for X component 16 divided by two equals eight, meaning we get eight square roots of two for our component, the sign at 315 degrees S equals to negative squared of two divided by two from the unit circle. This means this simplifies to negative a square of two. We can now write our vector, our vector will be V equals eight squares of two, I minus eight squares of two ja we can then notice the answer to our problem is answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 12, θ = 225°