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3Opción A

2,5 puntos

solo hay que contestar una de las dos opciones (A ó B).

Dados los puntos A(4,3,3)A(4, 3, 3), B(3,3,4)B(3, 3, 4), C(1,0,4)C(1, 0, 4) y D(4,0,1)D(4, 0, 1),
a
Justifica de forma razonada que los puntos AA, BB, CC y DD están en el mismo plano y halla la ecuación del plano que determinan.1 pt
b
Calcula el valor de kk para que el punto P(7,k,2)P(7, k, 2) esté en la recta rr que pasa por los puntos AA y CC.0,75 pts
c
Calcula la distancia del punto BB a la recta que pasa por AA y CC.0,75 pts

Formulario

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ANEXO TABLA DISTRIBUCIÓN NORMAL Tabla de distribución normal N(0,1)N(0,1) F(z)=P(Z≤z)F(z)=P(Z\leq z)
Anexo: curva de la distribución normal N(0,1), con el área F(z) rayada desde menos infinito hasta z, situado a la derecha de 0.
zz0,000,01
0,00,50000,5040
0,10,53980,5438
0,20,57930,5832
0,30,61790,6217
0,40,65540,6591
0,50,69150,6950
0,60,72570,7291
0,70,75800,7611
0,80,78810,7910
0,90,81590,8186
1,00,84130,8438
1,10,86430,8665
1,20,88490,8869
1,30,90320,9049
1,40,91920,9207
1,50,93320,9345
1,60,94520,9463
1,70,95540,9564
1,80,96410,9649
1,90,97130,9719
2,00,97720,9778
2,10,98210,9826
2,20,98610,9864
2,30,98930,9896
2,40,99180,9920
2,50,99380,9940
2,60,99530,9955
2,70,99650,9966
2,80,99740,9975
2,90,99810,9982
3,00,99870,9987
3,10,99900,9991
3,20,99930,9993
3,30,99950,9995
3,40,99970,9997
3,50,99980,9998
3,60,99980,9998
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000
zz0,020,03
0,00,50800,5120
0,10,54780,5517
0,20,58710,5910
0,30,62550,6293
0,40,66280,6664
0,50,69850,7019
0,60,73240,7357
0,70,76420,7673
0,80,79390,7967
0,90,82120,8238
1,00,84610,8485
1,10,86860,8708
1,20,88880,8907
1,30,90660,9082
1,40,92220,9236
1,50,93570,9370
1,60,94740,9484
1,70,95730,9582
1,80,96560,9664
1,90,97260,9732
2,00,97830,9788
2,10,98300,9834
2,20,98680,9871
2,30,98980,9901
2,40,99220,9925
2,50,99410,9943
2,60,99560,9957
2,70,99670,9968
2,80,99760,9977
2,90,99820,9983
3,00,99870,9988
3,10,99910,9991
3,20,99940,9994
3,30,99950,9996
3,40,99970,9997
3,50,99980,9998
3,60,99990,9999
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000
zz0,040,05
0,00,51600,5199
0,10,55570,5596
0,20,59480,5987
0,30,63310,6368
0,40,67000,6736
0,50,70540,7088
0,60,73890,7422
0,70,77040,7734
0,80,79950,8023
0,90,82640,8289
1,00,85080,8531
1,10,87290,8749
1,20,89250,8944
1,30,90990,9115
1,40,92510,9265
1,50,93820,9394
1,60,94950,9505
1,70,95910,9599
1,80,96710,9678
1,90,97380,9744
2,00,97930,9798
2,10,98380,9842
2,20,98750,9878
2,30,99040,9906
2,40,99270,9929
2,50,99450,9946
2,60,99590,9960
2,70,99690,9970
2,80,99770,9978
2,90,99840,9984
3,00,99880,9989
3,10,99920,9992
3,20,99940,9994
3,30,99960,9996
3,40,99970,9997
3,50,99980,9998
3,60,99990,9999
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000
zz0,060,07
0,00,52390,5279
0,10,56360,5675
0,20,60260,6064
0,30,64060,6443
0,40,67720,6808
0,50,71230,7157
0,60,74540,7486
0,70,77640,7794
0,80,80510,8078
0,90,83150,8340
1,00,85540,8577
1,10,87700,8790
1,20,89620,8980
1,30,91310,9147
1,40,92790,9292
1,50,94060,9418
1,60,95150,9525
1,70,96080,9616
1,80,96860,9693
1,90,97500,9756
2,00,98030,9808
2,10,98460,9850
2,20,98810,9884
2,30,99090,9911
2,40,99310,9932
2,50,99480,9949
2,60,99610,9962
2,70,99710,9972
2,80,99790,9979
2,90,99850,9985
3,00,99890,9989
3,10,99920,9992
3,20,99940,9995
3,30,99960,9996
3,40,99970,9997
3,50,99980,9998
3,60,99990,9999
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000
zz0,080,09
0,00,53190,5359
0,10,57140,5753
0,20,61030,6141
0,30,64800,6517
0,40,68440,6879
0,50,71900,7224
0,60,75170,7549
0,70,78230,7852
0,80,81060,8133
0,90,83650,8389
1,00,85990,8621
1,10,88100,8830
1,20,89970,9015
1,30,91620,9177
1,40,93060,9319
1,50,94290,9441
1,60,95350,9545
1,70,96250,9633
1,80,96990,9706
1,90,97610,9767
2,00,98120,9817
2,10,98540,9857
2,20,98870,9890
2,30,99130,9916
2,40,99340,9936
2,50,99510,9952
2,60,99630,9964
2,70,99730,9974
2,80,99800,9981
2,90,99860,9986
3,00,99900,9990
3,10,99930,9993
3,20,99950,9995
3,30,99960,9997
3,40,99970,9998
3,50,99980,9998
3,60,99990,9999
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000