Do i need to vectorize all the images that I put on a illustrator artwor specially If i just want to crop
down this image. Can't I just leave the image as a jpg.
In addition to what Lutz said, you may use the Artboard (if you just have one image) or a Clipping Mask (or an Opacity Mask, or something else) to hide unwanted parts.
And then there is the destructive deed, with the relevant Clipping Mask selected:
1) In the Transparency palette/panel dropdown list select anything but Normal (Multiply is fine),
2) Object>Flatten Transparency, just keep the defaults including 100% Vector,
This should reduce the actual size of the image to the Bounding Box of the Clipping Path.
You can use the image as a raster image the jpeg is converted to a simple raster image or i you wish a normal image. It can not be cropped but it can be masked with a clipping mask.
And sometimes you do want to do this in Illustrator ir the clipping mask is on going to be a regular shape for instance and you might want al5er it later.
And then you do this later for instance