build: run vendoring script from src/rust

diff --git a/Makefile b/Makefile
index 3467d73..7a32c7c 100644
--- a/Makefile
+++ b/Makefile
@@ -191,4 +191,4 @@ clean:
 
 # When you vendor rust libs avoid duplicates
 vendor-rust-deps:
-	(cd external; ./vendor-rust.sh)
+	./external/vendor-rust.sh
diff --git a/external/vendor-rust.sh b/external/vendor-rust.sh
index 69756e5..0683f34 100755
--- a/external/vendor-rust.sh
+++ b/external/vendor-rust.sh
@@ -2,8 +2,9 @@
 #
 # Script for vendoring our dependencies, including the deps of core/alloc.
 #
-# This script must be called from the <git-project-root>/src/rust directory. It will place the
-# dependencies in a directory called "vendor" in the current working directory.
+# This script can be called from any directory. It runs Cargo from the
+# <git-project-root>/src/rust directory so rustup loads rust-toolchain.toml, and places the
+# dependencies in <git-project-root>/external/vendor.
 #
 # For some reason Cargo needs to find the dependencies of all rust std libs. Since "test" depends
 # on all the other ones, we take the toml-file from it. This means that we vendor libs that we
@@ -15,9 +16,16 @@
 # Copying the Cargo.lock file in the rust sysroot image requires root permissions. Therefore it is
 # done in the Dockerfile in our setup.
 
+SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
+REPO_ROOT="$(cd "$SCRIPT_DIR/.." && pwd)"
+RUST_WORKSPACE_DIR="$REPO_ROOT/src/rust"
+VENDOR_DIR="../../external/vendor"
+
+cd "$RUST_WORKSPACE_DIR"
+
 RUST_SYSROOT="$(rustc --print=sysroot)"
 
 RUSTC_BOOTSTRAP=1 cargo vendor \
-    --manifest-path ../src/rust/Cargo.toml \
+    --manifest-path Cargo.toml \
     --sync "$RUST_SYSROOT/lib/rustlib/src/rust/library/test/Cargo.toml" \
-    vendor
+    "$VENDOR_DIR"