Begin2.DVI

I6-12. (c) 23 / 9 (d) 23 / 3

I6-13. (a) ˆeC=ˆe^2 √+ ˆ 2 e^3 also−ˆeC (b)− 1 /

√

3

I6-14. (b)A~·ˆeα=−cosα+

√

3 sinα

(c)α=π/ 6 or 7 π/ 6

(d)y(α) =

√

3 sinα−cosαand

dy

dα= 0whenα=−π/^3 or^2 π/^3

y′′(α) =−

√

3 sinα+cosα,y′′(−π/3)> 0 andy′′(2π/3)< 0 , Maximum +2, Minimum

-2

I6-15.

A~(t) =A~ 0 +A~ 1 (t−t 0 ) +A~ 2 (t−t^0 )

2

2! +

A~ 3 (t−t^0 )

3

3! +···+

A~n(t−t^0 )

n

n! +···

A~′(t) =A~ 1 +A~ 2 (t−t 0 ) +···+A~n(t−t^0 )

n− 1

(n−1)! +···

A~′′(t) =A~ 2 +A~ 3 (t−t 0 ) +···+A~n(t−t^0 )

n− 2

(n−2)! +···

..

.

..

.

Evaluate the derivatives att=t 0 and show

A~(t 0 ) =A~ 0 , A~′(t 0 ) =A~ 1 , A~′′(t 0 ) =A~ 2 , ... , A~(n)(t 0 ) =A~n, ...

I6-16. (a)A~×B~=− 16 ˆe 1 + 8ˆe 3 (b) 16 ˆe 1 − 8 ˆe 3 (e)θ= cos−^1 (11/21)≈ 58. 41 ◦

I6-17.

D~ 1 =A~+B~= 3ˆe 1 + 11ˆe 2 + 4ˆe 3

D~ 2 =B~−A~=ˆe 1 + 7ˆe 2

Area=|A~×B~|= 15

I6-18.
cosα=

√

2 / 2

cosβ=1/ 2

cosγ=− 1 / 2

~e=~ρ

|~ρ|

= cosαˆe 1 + cosβˆe 2 + cosγˆe 3

cos^2 α+ cos^2 β+ cos^2 γ= 2/4 + 1/4 + 1/4 = 1

I6-19. IfA~×B~=~ 0 , thenA~is parallel toB~ orA~=cB~ for some constantc.

Solutions Chapter 6