The sheet-like body that cuts across rock layers and is produced when magma is injected into a fracture is called a dike.

Here's why:

* Dike: A dike is a tabular (flat and sheet-like) intrusion of igneous rock that cuts across existing rock layers. It forms when magma forces its way into cracks and fissures, solidifying in place.

* Magma Injection: The process of magma being forcefully injected into existing rock formations is called intrusion.

* Fracture: A fracture is a crack or break in the rock.

Other related terms:

* Sill: A sill is another type of igneous intrusion that is parallel to the existing rock layers.

* Batholith: A large, irregular mass of intrusive igneous rock that is often associated with mountain ranges.

Let me know if you have any other questions!