What is the difference between a unit vector and a vector component?

Please clearly explain it because I've googled this question, searched forums, and watched youtube videos and I can't get an explanation I can understand. I have a homework problem asking if (i + j + k) is a unit vector, and the back of the book says it is not. Why not? What is it? what would make it a unit vecor?|||i+j+k has both a magnitude and direction. It _is_ a vector.





A Unit vector is a vector of magnitude 1. i+j+k doesn't have magnitude 1.





This might help you in vector addition: i+j+k is the sum of i, j and k


http://www.ucl.ac.uk/Mathematics/geomath…





We need to divide the vector by its magnitude to make it a unit vector, since it will have magnitude one then. So, the unit vector in the direction of i+j+k is: (i+j+k)/sqrt(3)|||I'm not entirely sure,


But a vector must have both magnitude (a value) and direction. i + j + k will give a value but no direction, therefore it can't be a vector.





This is irrelevant, but the components of a vector are simply the x difference value and the y difference value. This is found by using pythagoras and the tangent ratio and is used to add two vectors together.