In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i ...

Question

In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.

||2u||

Accepted Answer

Considering the vector A equals 11 I minus four J determine the following scalar where we have the magnitude of five A. And we have four possible answers with three squares at 3 five square roots of 1 37 three square roots of 69 a square root of 201. Now to solve this, let's first find what vector five A is. So we have five A questions. We have a scale or multiple. The scalar multiple just means we will multiply every component of the vector by the scale of multiple K which in our case is five, other words, you will have five A S equals to five multiplied by I minus four J. This gives us five multiplying 11 or 55 I five, multiply negative four T negative 20 J. Now this is our vector five A to which we need the magnitude A vector normally is given in the form A I plus B J. If we have this form, we can take the square root of the squared components and add them together. In other words, the magnitude of vector V, it equals to A squared. Plus B squared. In our case, our A is 55 and R B is negative we should get the square of 55 squared plus negative 20 square 55 squared is 30 and negative 20 squared is 400 which we add those together to get the square root of 34 25. This factors to the square root of multiplied by 1 37 which we can take the square root of 25 to just get five square roots of 137. We can't simplify any further. So our answer corresponds to answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
||2u||

Key Concepts

Vector Magnitude (Norm)

Scalar Multiplication of Vectors

Properties of Vector Norm under Scalar Multiplication

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