Exercise 5

If two vectors are orthogonal, their dot product is zero.

\[\vec{a} \cdot \vec{b} = 2-1+3 = 4\]

\[\vec{a} \cdot \vec{c} = 3+1+0=4\]

\[\vec{a} \cdot \vec{d} = -3+0+2=-1\]

\[\vec{b} \cdot \vec{c} = 6-1+0 = 5\]

\[\vec{b} \cdot \vec{d} = -6+0+6 = 0\] \[\vec{c} \cdot \vec{d} = -9+0+0 = -9\]

Vectors \(\vec{b}\) und \(\vec{d}\) are orthogonal.