Writing Vector <1,7> as Sum of 2 Vectors

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To express the vector <1,7> as a sum of two vectors, one parallel to <2,-1> and one perpendicular to it, the solution involves using vector decomposition. The first vector, parallel to <2,-1>, is calculated as <3,6>, while the second vector, perpendicular to <2,-1>, is <-2,1>. The dot product is relevant for confirming the orthogonality of the perpendicular vector. Visualizing the vectors as forming a right-angle triangle can aid in understanding the solution. This method effectively resolves the problem of vector decomposition.
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Homework Statement



Write the vector <1,7> as a sum of two vectors, one parallel to <2,-1> and one perpendicular to <2,-1>

Homework Equations


DOt Product


The Attempt at a Solution



I'm confused on where to begin this problem. Should I be using the dot product?

Thanks
 
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i think you should draw out the vectors as they make up a right angle triangle.
 
I got the answer:

<-2,1> and <3,6>
 

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