In Exercises 61–64, find the magnitude ||v||, to the nearest h...

Question

In Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = (4i - 2j) - (4i - 8j)

Accepted Answer

Bind the magnitude and direction angle of the vector. A given below express your answer to one decimal place where we have A equals seven I minus three J minus seven I minus 13 J. He had four possible answers all with different magnitudes and direction angles. Now to solve this, let's first simplify our vector A. We can do this by multiplying our negative over to both the seven I and the negative 13 J. We have seven I minus three J and then we have minus seven I plus 13 J. After we distribute our negative, we can now add our I S and J components together. We get seven I minus seven I which gives us zero I negative three J plus 13 J gives us plus 10 J. Since we have zero I, our vector simplifies down to just 10 J. Now we need to find the magnitude of the vector. The magnitude is given by the sum of the squared components of our vector all underneath the square root. So we can write the format like this with double vertical bars around A, this is the square root of our X component squared plus our Y component squared. Where in our vector, our vector is the form X I plus Y J or magnitude thin will be zero squared plus squared all underneath the square root that gives us a square of 100 which simplifies to just 10. Now, we have our direction, our direction is given by the inverse tangent of our Y component divided by our X component. We get the inverse tangent of 10 divided by zero. Now 10 divided by zero is undivided. However, in the tangent function, there is an angle which is undefined or which has our components undefined. I should say that angle happens at 90 degrees. If we were to graph our tangent function, we would notice we have an Asymptote at 90 degrees. So we now have our magnitude of 10 and our direction of degrees which corresponds to answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = (4i - 2j) - (4i - 8j)

Key Concepts

Vector Subtraction

Magnitude of a Vector

Direction Angle of a Vector

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