{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Hoja1","Hoja2","Hoja3"],"not_rendered":{"charts":0,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Hoja1","index":0,"n_rows":53,"n_cols":14,"rows_kept":53,"cut":false,"hidden":false,"merged":[[36,0,36,13],[42,0,42,13],[48,0,48,13],[0,0,0,13],[6,0,6,13],[25,0,25,13],[30,0,30,13],[15,0,15,13],[20,0,20,13]]}
["Suma de vectores"]
[]
["A = ",4,4,7,null,"A + B =  ",{"$f":"B3+B4","v":18},{"$f":"C3+C4","v":-14},{"$f":"D3+D4","v":28},null,"A + B =  ",{"$f":"B3:D3+B4:D4","v":18},-14,28]
["B = ",14,-18,21]
[]
[]
["Producto por un escalar"]
[]
["A = ",4,4,7,null,"aA + bB =",{"$f":"$B$12*B9+$B$13*B10","v":64},{"$f":"$B$12*C9+$B$13*C10","v":-64},98,null,"aA + bB =",{"$f":"B12*B9:D9+B13*B10:D10","v":64},-64,98]
["B = ",14,-18,21]
[]
["a=",2]
["b=",4]
[]
[]
["Magnitud de un vector 2D"]
[]
["A = ",4,4,null,null,"|A|=",{"$f":"SQRT((B18)^2+(C18)^2)","v":5.6568542494923806},null,null,null,"|A|=",{"$f":"SQRT(SUMPRODUCT(B18:C18,B18:C18))","v":5.6568542494923806}]
[]
[]
["Dirección vector 2D"]
[null,null,null,null,null,null,"Rad",null,null,null,null,"Grados"]
["A = ",4,-4,null,null,"qx = ",{"$f":"IF(AND(B23>0,C23>0),ATAN(C23/B23),IF(B23<0,PI()+ATAN(C23/B23),IF(AND(B23>0,C23<0),2*PI()+ATAN(C23/B23),IF(AND(B23=0,C23>0),PI()/2,IF(AND(B23=0,C23<0),3*PI()/2,0)))))","v":5.497787143782138},null,null,null,"qx = ",{"$f":"G23*180/PI()","v":315}]
[]
[]
["Magnitud de un vector 3D"]
[]
["A = ",4,4,7,null,"|A|=",{"$f":"SQRT((B28)^2+(C28)^2+(D28)^2)","v":9},null,null,null,"|A|=",{"$f":"SQRT(SUMPRODUCT(B28:D28,B28:D28))","v":9}]
[]
[]
["Ángulos directores 3D"]
[null,null,null,null,null,null,"Rad",null,null,null,null,"Grados"]
["A = ",4,4,7,null,"qx = ",{"$f":"ACOS(B33/SQRT(SUMPRODUCT(B33:D33,B33:D33)))","v":1.1102423351135742},null,null,null,"qx = ",{"$f":"G33*180/PI()","v":63.61220003875701}]
[null,null,null,null,null,"qy = ",{"$f":"ACOS(C33/SQRT(SUMPRODUCT(B33:D33,B33:D33)))","v":1.1102423351135742},null,null,null,"qy = ",{"$f":"G34*180/PI()","v":63.61220003875701}]
[null,null,null,null,null,"qz = ",{"$f":"ACOS(D33/SQRT(SUMPRODUCT(B33:D33,B33:D33)))","v":0.67967381890824385},null,null,null,"qz = ",38.942441268981383]
[]
["Producto punto"]
[]
["A = ",4,4,7,null,"A . B = ",{"$f":"B39*B40+C39*C40+D39*D40","v":131},null,null,null,"A B = ",{"$f":"SUMPRODUCT(B39:D39,B40:D40)","v":131}]
["B = ",14,-18,21]
[]
[]
["Producto cruz"]
[]
["A = ",4,4,7,{"$f":"B45","v":4},{"$f":"C45","v":4},null,null,null,null,"A x B = ",{"$f":"MDETERM(C45:D46)","v":210},{"$f":"MDETERM(D45:E46)","v":13.999999999999988},{"$f":"MDETERM(E45:F46)","v":-128}]
["B = ",14,-18,21,{"$f":"B46","v":14},{"$f":"C46","v":-18}]
[]
[]
["Triple producto escalar"]
[]
["A = ",4,4,7,null,"A.(BxC)=",{"$f":"MDETERM(B51:D53)","v":306}]
["B = ",14,-18,21]
["C = ",2,1,1]

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{"sheet":"Hoja3","index":2,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}