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creating seeking algorithm with info availiable

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if i have my starting vector, the point im starting/currently at, and the destination vector,and a speed vector( just a vector with x=1,y=0 and z=1) the point im trying to navigate to, how do i use both to allow my charachter to arrive at the destination? i have been normalizing the destination and multiplying my start point by this but it doesnt work, and i have no idea what to do next . im trying to create a seek algorithm but i dont know what kind of maths i use to create a formula that allows my charachter to continually check its position and slow down as it nears its target until it stops on its target. it would be greate to find out how to do this as i will have to do the same kind of thing for a repulsion algorithm. sorry if i use the term vector instead of point, but i have the points stored in vectors so i just got into the habit of calling them that.

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