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Chapter 6: Problem 10

Suppose \(\mathbf{u}=(-3,2)\) and \(\mathbf{v}=(-2,-1)\) (a) Draw a figure using arrows illustrating the difference \(\mathbf{u}-\mathbf{v}\) (b) Compute the difference \(\mathbf{u}-\mathbf{v}\) using coordinates.

Short Answer

Expert verified
(a) To draw the difference between two vectors, first draw the vectors \(\mathbf{u}\) and \(\mathbf{v}\) originating from the same point. Then, draw the vector \(\mathbf{u}-\mathbf{v}\) by connecting the tail of -\(\mathbf{v}\) to the tail of \(\mathbf{u}\). (b) To compute the difference between the two vectors in terms of coordinates, subtract their respective components: \(\mathbf{u}-\mathbf{v}=(-1,3)\).

Step by step solution

01

(a) Drawing Vectors Using Arrows

To draw the difference between two vectors, we can follow these steps: 1. Draw the vector \(\mathbf{u}\) originating from the point O, which is (-3,2). 2. Draw the vector \(\mathbf{v}\) originating from the same point as \(\mathbf{u}\), which is (-2,-1). 3. Draw the vector \(\mathbf{u}-\mathbf{v}\) which is equal to \(\mathbf{u}\) + (-\(\mathbf{v}\)). You can obtain this by drawing the vector -\(\mathbf{v}\) originating from the tip of vector \(\mathbf{u}\) and then connecting the tail of the -\(\mathbf{v}\) vector to the tail of vector \(\mathbf{u}\).
02

(b) Computing the Difference in Coordinates

To compute the difference between the two vectors, we can subtract their respective components: Step 1: Find the difference of the x-components. \((-3)-(-2)=(-3+2)=-1\) Step 2: Find the difference of the y-components. \(2-(-1)=(2+1)=3\) Step 3: Combine the differences of the x-components and y-components to get the coordinate representation of the difference between the vectors. \(\mathbf{u}-\mathbf{v}=(-1,3)\)

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