express skew-commutative product of Whitney sum of vector bundles in tensor products

Question

Let $\xi$ and $\eta$ be vector bundles over a paracompact space $B$ and $\xi\oplus\eta$ be their Whitney sum. Can we write $\Lambda(\xi\oplus\eta)\cong \Lambda(\xi)\otimes \Lambda(\eta)$ as (graded) vector bundles?

For vector spaces $V,W$, we have $\Lambda(V\oplus W)\cong \Lambda(V)\otimes \Lambda(W)$ are isomorphic as graded vector spaces. But I am confused for vector bundle case...