hey mate,

In relation to (a), (b), for any two 3 Dimensional vectors of the form

v1 = a1*i + b1*j + c1*k, v2 = a2*i + b2*j + c2*k

Their Euclidean Inner or 'Dot' Product is calculated using either

(i) v1 . v2 = a1*a2 + b1*b2 + c1*c2

(ii) v1 . v2 = |v1|*|v2|*cos(y) where y is the angle between v1 and v2

Since the angle is unknown I would recommend using (i)

Their Cross Product is defined as,

v1 X v2 = det(A), where A is a 3x3 matrix where the first row of A = (i,j,k), the second row is v1 and the third is v2

For (c)

As before for a given three dimension vector of the form v1 (as defined previously)

Scalar Multiplication -

m*v1 = m(a1*i + b1*j + c1*k) = m*a1*i + m*b1*j + m*c*k

Addition

v1 + v2 = (a1 + a2)*i + (b1+b2)*j + (c1 + c2)*k

Hope this helps,

Let me know if you require any further assistance,

Regards,

David