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. 3.1.

§ 3.7.

§ 2.3. X, Y, Z (. 3.1)

R=J¥+W+. Q = arctg()/X), q)=arccos(Z/y?),

R - , Q - ( - .

X = Rs\n(fcosQ, Y = R (f cos Q, Z~ = R cos .

, Z = 0, = 90°, .

3.62. >

10 PRIHTnPEOEPftSOBAHME

20 PRIMTC«rePM4ECK< - 0

38 PRINT - 1

40 ASIF ft=l THEN 110 . !

50 R=R

60 1 -) 6=QtLETQl=RftD<Q)

70 -) F=F!LEtFl=RAD<F>

80 LETX=RieSIH<Fl>«C0S<Ql>tLETV=R9iSIH<Fl)9iSIN<Ql)

98 LETZ=R«COS<Fl>sPRIHTflEKftPTOBM

100 PRIMTX=Xj-V=V»Z=Z5ST0P

110 X,V»Z X»V,Z

120 LETR=SaR<X*X+V*V+Z9i2>!LETFsACS<Z.R)!LETe=ATNCV.X>

130 PRIHT R=R, " <a=IiE6«a)

14 PRINT =6<)!

. = 10, (3 = 40° = = = 60° ( 0) =6,634139482, )= = 5,566703992 2 = 5, X=)=Z=10 ( 1) =17,32050808, Q = 45° = =54,73561032°.

(. 3.2) ( =()

X=(X - Մ) cos ?+() - Id) si Q, r={Y- )) cos(3-(X-X.,) sin Q,

X Y - (X, V), Id - . 3.83.


; 3.2.

10 *;

20 ) G=G

30 LETO=RftIi«»! INPUT XSVO ..

40 XV XV

45 LETXl=<X-B)i«COSCG>+<V-C)ii!SIN<Q): :

50 LETVl=<V-C)ii!COSC<a>-CX-B)ii!SIN<G> . :

60 PRINT

70 PRIHTXl=XlrV1=V1!&0T0 40!EHII

. Q = 20°, Xn = 3, ( = 2, = 5 =5

X =2,905445672 )" =2,135037676.

() (Xi, ) (, ),

, .

?=/(X2-xo+(2-y,)

(X, ), M/N:-

J NX,+MX2 Ny\+MY2 =-..... . =-

./ + /

/ + /



PRINT

INPUT 1 KItVI

38 INPUT 2 ;.!2»V2

40 LETIi=SGR( (2-1 >-2+(V2-Vl>2J

50 PR I NT Ii=Ii

60 INPUT MjH M,H

70 LETX= < N*;>! 1+2 V t M+N >

80 LETV=<N«V 1 +M*V2>/a-1+N>

90 PRINT

100 PRINTK=K,V=V:END

;>UtV1

;>!2,V2

. X, = 2.3, 1=4, 2 = 8.5 2 = 0,7 D = 7.023531875. = 3 /= 2, = 6,02 )=2,02.

+ + BY-\-C = 0, (. 3.3), (0,0)

=1//

Q,

cos Q=+A/Ja + B\ sin Q=+B/Ia + B\

- , > , +, <0.

3.65.

++


. 3.3.

10 PRINT ++=0

20 INPUT ,, (\,,

30 LETD=1!IF >0 THEN LETII=-1

40 LETF=SQR +>:LETP=ABS<>/F

50 PRINT <0/0) =

60 PRINT08()=/, SlH<Q)=Ii*B/F

70 PRINTyrofl Q=IiEGCACS<D»ft-F>):EHD

. =3. =-4 =10 = 2, cos(3=-0,6, sin (3 = 0.8 (3=126,8698976°.

(0,0,0) (X, Y, Z)

a = arccos (X/D), p = arccos (Y/D)

= arccos (2/D). 3.66.

10 PRINT Ź

20 INPUT K/VZ X,V>Z

30 LETD=S(aR < +V*V+Zii!Z > s LETA=X/ti: LETB=VD: LETC=Z>Ii

40 PRINTCOS =,COS EETA=B/COS =

50 PRINTftj1b4>A=DE&i:ftC:StA>)>EETft=i)EG<ACS<:B>>,

60 PRINTrAMMA=DEG<ACS<C>>".&OTO 2esEND



. = 2. Y=~2 Z= -1 cos = 0,666666667, cos = = -0,666666667, cosv=-0,333333333, = = 48,189685, = 131,8103149° v = = 109.4712206°.

(0,0,0) {\, Vi, Zi) (, Y2, Z2) (. 3.4)

X,X2+Y,Y2 + Z,Z2 Q = arccos - -

Vxf+yf+z! -sIxl+Yl+zl

, -,

D={X,-X2f+(Y,-Y2f + {Z,.

(X, Y, Z), M/N,

NX, + MX2 M + N

NZ,+MZ-, " M + N

NYi+MY2 M + N


. 3.4. , , (, , 0)

3.67.

10 PRINTVrOn , !--

£@ PRINTHK ,

30 PRINT WW

40

50 INPUT;>!bVb21 ,,

60 PRINT

70 IHPUT;>S,V£,Z£ Ii,E,F

80 LETS=SQRtA-IO"£+(-)£+<C-F)>

90 LETG=SQR(++)*SQR(++)

100 =<11++)

110 1!.0 ! <) G=DE&CftCS(G.O)

120 Ii=S

130 1 , M,H!LETR=M+H

140 LETL=A!LETK=D!GOSUB 190!LETX=W

150 LETL=B;LETK=E!GOSUB 190:LETV=ll

160 LETL=C:LETK=F:GOSUB 190!LETZ=W

170 PRINT

180 PRIHT;>!=;>!,V=V,2=2!G0T0 13©

190 LETW=(H*L+M*KVR:RETURN:ENE

. A\ (8; -3; 8) A2 (6; -1; 9) (3=14,6712486° D = 3. =1 /= 4, = 7,6, =-2,6 2 = 8,2.

, AX + BY + CZ+D = U, (. . 3.5)

p=!Di/Ve+c-.

a = arccos (//+ + ), B=arccos (

= rccos (+ C/V +),

- (0,0,0) , , V - ( , (0,0,0) ).


/(

. 3.5. ,



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