a vector is a shape,and it can be resized without loosing any quality like a jpeg picture would for example. in other words you can select a vector and resize it from small to large than small than enlarge it again any times you want to without it loosing the quality. this is the simplest way to explain a vector graphic I guess.. get it?
its not how you make it..it just has to be a vector shape,you can do it in photoshop,illustrator or some other program... I just wanted you to see the difference between a pixel image and a vector image.. here's something you can do to see it in action.. open a picture in photoshop, hover the mouse onto the layers tab (right lower corner),right click on the layer and click "layer from background" and hit enter,then press ctr+t to resize the picture,grab one of the corners and when the two sided arrow appears click and drag inwards to make the image smaller and hit enter. then ctr+t again and this time do the same but this time resize it..there... see how the image lost its quality? that's because that's what happens with pixel image
well in PS you cand do it with the pen tool (checked "shape layers") and with the shapes tools (rectangle,ellipse,polygon... ),in the layers tab you can see the names of the layers as "shapes" as you create them and in illustrator almost everything is vector I just don't have it installed at the moment to tell you the steppes
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