The Planes X + 2y + Z = and 3x

question 566

Essay

The planes x + 2y + z = and 3x + y - 2z = intersect in a line. Determine the point on this line of intersection for which x = .

---

Definitions:

Hot Spots

Areas of the Earth's mantle that are anomalously hot compared to surrounding areas, causing volcanic activity on the surface.

Linear Island Chains

Linear arrangements of islands, often volcanic, aligned along a single submarine ridge due to tectonic activity.

Oceanic Plateaus

Large, flat, elevated areas of the seabed, formed by volcanic activity and often found in the deep ocean.

Mantle Plumes

Columns of hot, solid material that rise from deep within the Earth's mantle and can cause volcanic hotspots.