Answer to Question #59910 in Math for joseph ogala

Question

If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj

. evaluate
ddt(A⋅B)

If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj

. evaluate
ddt(A×B)

If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj

. evaluate
ddt(A⋅A)

If
A=sinui+cosuj+uk
A=sin⁡ui+cos⁡uj+uk
,
B=cosui−sinuj−3k
B=cosui−sinuj−3k
and
C=2i+3j−k
C=2i+3j−k

, evaluate
ddu(A×(B×C))
ddu(A×(B×C))
at u=0

Let
A=x2yzi−2xz3j−xz2
A=x2yzi−2xz3j−xz2
and
B=4zi+yj+4x2k
B=4zi+yj+4x2k

, find
∂2∂x∂y(A×B)
∂2∂x∂y(A×B)
at (1,0,-2)

solve
d2Adt2−4dAdt−5A=0