Question

find the triple scalar product u . (v * w) for the vectors
u= (5, 9, -6)
v= (5, 8, -1)
w= (-2, 8, 3)

Answer 1

if by v * w , you mean
v X w , the cross product, then

v X w = (5, 8, -1) X (-2, 8, 3)
= (32, -13, 56) , I assume you know how to find the cross-product

Then u . (v * w)
= (5, 9, -6) . (32, -13, 56)
= 160 - 117 - 336
= - 293

Answer 2

u • v × w is just the determinant

|5 9 -6|
|5 8 -1|
|-2 8 3|