Answer to Question #59909 in AJAX | JavaScript | HTML | PHP for joseph ogala

Question

Determine the unit tangent at the point where t=2 on the curve
x=t2+1
x=t2+1
,
y=4t−3
y=4t−3
and
z=2t2−6t
z=2t2−6t

.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