Assignment No.1: Exercise 3 and 4 (Section 12.4 Exercise 50)

load(vect);

Exercise 2 and 3 are designed together to prove the equation of vector triple product. Instead, we can show the equation directly and symbolically.

First define three vectors aa, bb, cc, symbolically.

aa: [a[1],a[2],a[3]];

bb: [b[1],b[2],b[3]];

cc: [c[1],c[2],c[3]];

The dot product and the cross product can be carried out symbolically.

aa . bb;

express(aa ~ bb);

The left-hand side of the vector triple product formula can be calculated symbolically.

dd: express(aa ~ (bb ~ cc));

The right-hand side of the formula can be similarly calculated symbolically.

ee: (aa.cc)*bb - (aa.bb)*cc;

To see that the left-hand side equals the right-hand side, we expand their symbolic calculation.

dd: expand(dd);

ee: expand(ee);

Or, you can find their difference equal to zero vector.

dd - ee;

Thus, we have proved the vector triple product formula directly.