SageMath syntax for Section 2.2

SageMath is a free open-source mathematics software system. You can use a SageMath cell online by going here.

The syntax described in section 2.1 generalizes to vectors in 3-space. Simply append a third component to your vectors.

• v=vector([2,3,1]) --- Define the vector $\vec{v}=\langle 2, 3, 1 \rangle$.
• v.norm() --- Magnitude of $\vec{v}$.
• v.normalized() --- Unit vector with the direction of $\vec{v}$. Same as $\vec{v}/\|\vec{v}\|$.
• v=vector([2,3,1]); u=vector([-5,4,-2]); 3*v-2*u --- Compute the vector $3\vec{v}-2\vec{u}$.
• plot(v,color="red") --- Plot the vector $\vec{v}$ in red.
• a=plot(v,color="red"); b=plot(u,color="blue"); show(a+b) --- Plot $\vec{v}$ and $\vec{u}$.