written assignment I, Assignments of Mathematics

Answer for written assignment in Calc III

Typology: Assignments

2024/2025

Uploaded on 06/30/2026

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Q
,
let
M
=
W
,
we
Ws
where
[WSWWs
I
U
,
Uz
Us
[V
,,
V2
,
V3
Y
Iv
,
V2
Vs
We
can
represent
the
quantity
D
:
D
=
defM
=
W
,
(UcVs-UsV2)
-
Wa(k ivs-
U3V)
+
Ws(U
,
V2-UzV
,
S
=
W
.
/keVs
-
UsVz]
+
Wa
/UsV
,
-
U
,
Us)
+
Ws)
U
.
U2
-
UzV
,
)
=
<W
,,
Wa
,
Ws)
·
[UcVs
-
UsVz
,
UzV
,
-
U
,
Us
,
U
.
U2-UzV
,
>
=
.
(nx
)
Yand
8
he
on
the
Xy-plane
.
Then
EXV
is
in
the
same
direction
as
Dididate
a
pet
Z
11
Project
Foll
=
111
cost
=
Height
We
have
&
I
Note
that
ixt
is
orthogonal
to
the
base
formed
by
it
and
Hence
D
gives
the
height
of
the
parallelopped
formed
by
i
, ,
i
.
&
i
.
/xi)
=
11
will
cost
11
EXT11
Idef
of
dot
product)
=
Volume
of
parallelopped
/
given
Thus
sume
=
Aread-base
=
pf2

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Q (^) ,

let M =

W (^) , we Ws where

U , Uz Us I [WSWWs

[V,, V2 (^) , V3 Y

Iv

, V2^ Vs

We can represent the^ quantity D^ :

D =^ defM =^ W^ , (UcVs-UsV2) -^ Wa(kivs-^ U3V)^ +^ Ws(U, V2-UzV, S

= (^) W (^). /keVs - UsVz] + (^) Wa (^) /UsV (^) , - U (^) , Us) + (^) Ws) U. U2 - UzV (^) , ) = (^) =. (nx) Yand 8 he on the (^) Xy-plane.

Then EXV^ isin^ the^ same direction^ as

Dididate

a

pet Z

11 Project Foll =^111 cost^ =

We (^) have (^) Height &

I

Note thatixt^ is (^) orthogonal to the base formed (^) by it and Hence (^) D gives the^ height^ of the (^) parallelopped formed by

i, ,

i . & (^) i. /xi) = (^11) will cost 11 EXT11 Idef (^) of dot (^) product)

=Volume^ of parallelopped /

given Thus sume

= Aread-base =
Q
Y let u = < a , 0) and 8 =< b . c).
The width of the

parallelogram is moix Area = 10.^ h =^ ac = det 1 e

= (^2) : 0 ,, no =

E, it
3. =^2. 40 , 8 ,+ to (base &

height are^ constant) g = Ar, + to