Question Video: Writing a Vector Represented Graphically in Terms of Fundamental Unit Vectors | Nagwa Question Video: Writing a Vector Represented Graphically in Terms of Fundamental Unit Vectors | Nagwa

# Question Video: Writing a Vector Represented Graphically in Terms of Fundamental Unit Vectors Mathematics • First Year of Secondary School

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The given figure shows a vector π in a plane. Express this vector in terms of the unit vectors π’ and π£.

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### Video Transcript

The given figure shows a vector π in a plane. Express this vector in terms of the unit vectors π’ and π£.

Weβre asked to express the vector shown in the graph in terms of the fundamental unit vectors π’ and π£. So letβs remind ourselves what these look like in the Cartesian plane. π’ is a horizontal vector and π£ is a vertical vector, and they both start at a given origin traveling in the positive π₯- and π¦-directions, respectively, with length equal to one.

Now, to express the vector π in terms of π’ and π£, we need to consider its π₯- and π¦-components separately. So letβs begin with the π₯-component. From the graph, we see that the π₯-component is equal to negative three. Using the horizontal unit vector π’, which is going in the positive π₯-direction, we flip this unit vector so it becomes negative, as itβs now pointing in the negative π₯-direction. And to reach π₯ is negative three, weβre adding three copies of negative π’. This tells us that the π₯-component of π in terms of the fundamental unit vector π’ is negative three π’.

Next, considering the π¦-component of π, we see that this is positive two. And we can produce this by adding two copies of π£. Hence, the π¦-component of vector π in terms of the fundamental unit vector π£ is two π£.

So now adding the two components together, where by convention we write the π₯-component first, we have π equals negative three π’ plus two π£.

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