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We set up vectors in a way which is slightly different from how we do it in Maple.
![\begin{maximasession}
a: [1,2,3];
b: [2,-1,4];
\maximaoutput*
\i1. a: [1,2,3];...
...\\
\i2. b: [2,-1,4]; \\
\o2. \left[ 2 , -1 , 4 \right] \\
\end{maximasession}](img11.png)
We can do the standard addition and scalar multiplication of vectors.
![\begin{maximasession}
3 * a;
a + b;
\maximaoutput*
\i3. 3 * a; \\
\o3. \left[ 3...
...right] \\
\i4. a + b; \\
\o4. \left[ 3 , 1 , 7 \right] \\
\end{maximasession}](img12.png)
The dot product operator is a simple period "." between the vectors.
We can check our answer to make sure it is right.
To do cross products we must load a special package, the vect package, which is included with Maxima.
The symbol for the cross product is the tilde "~" up on the left corner of the keyboard (you need to do Shift to get it).
![\begin{maximasession}
a b;
express(%);
\maximaoutput*
\i8. a b; \\
\o8. \l...
...\\
\i9. express(%); \\
\o9. \left[ 11 , 2 , -5 \right] \\
\end{maximasession}](img16.png)
The cross product did not look like anything at the beginning; we had to express the cross product to get something recognizable.
The norm (length) of a vector is the square root of the dot product of the vector with itself.
Putting what we have learned all together we may do vector projections and scalar triple products (we will need another vector c for the STP to make sense).
![\begin{maximasession}
(a . b)/(a . a) * a;
c: [-5, 2, 9];
a . (b c);
express(%...
..., -9 \right] \right) \\
\i14. express(%); \\
\o14. -96 \\
\end{maximasession}](img18.png)
Again, we needed to express the cross product to get anything useful.