Answer to Question #195641 in Differential Geometry | Topology for Fatowore Samson

Question

If

G

â

ƒ

—

=

ã

€

–

5

t

ã

€

—

2

i

+

t

j

−

t

3

k

G⃗=〖5t〗2i+tj−t3k and

F

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ƒ

—

=

s

i

n

t

i

â

€

“

c

o

s

t

j

F⃗=sinti–costj, what is

d

/

d

t

(

G

×

F

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ƒ

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)

d/dt(G×F⃗)

Answer 1

$G=-2i+tj-3tk$

$F=isint+jcost$

$G\times F=\begin{vmatrix} i & j&k \\ -2 & t&-3t \\ sint&cost&0 \\ \end{vmatrix}=3ticost-3tjsint-(2cost+tsint)k$

$\frac{d}{dt}(G\times F)=(3cost-3tsint)i-(3sint+3tcost)j-(sint+tcost-2sint)k=$

$=3(cost-tsint)i-3(sint+tcost)j-(tcost-sint)k$