Let A=ia1 + ja2 + ka3
B= ib1 +jb2 =kb3 and
C=ic1 + jc2 +kc3
B.C =b1c1 + b2c2 +b3c3 is a scaler and so
A.(B.C) = (b1c1 + b2c2 +b3c3)(ia1 +ja2 +ka3)
A.(B.C) = ia1b1c1 +ja2b2c2 +ka3b3c3 . . . . . . . . . . .(1)
A.B = a1b1 + a2b2 +a3c3 is a scaler and
(A.B).C = (a1b1 + a2b2 +a3c3)(ic1 + jc2 +kc3)
(A.B).C = ia1b1c1 + ja2b2c2 + ka3b3c3 . . . . . . . . . . (2)
RHS’s of (1) and (2) are identical and so
the LHS’s should be equal and hence it follows that
A.(B.C) = (A.B).C
It'd be a or b. it says, " i'm a programmer. my feild of study is ___ "
a is, " computing "
b is, " graphic arts and design "
and c, and d wouldn't work because they're " biology " and " health science "
1. “Yo busque la mochila...”
2. “Ella tenía dos años...”
3. “Vives tu en...”
Hola, Omar: Como tú no pudiste¹ venir a mi fiesta de cumpleaños, quiero contarte cómo fue. El día de mi cumpleaños, muy temprano por la mañana, mis hermanos me dieron² una gran sorpresa: ellos dejaron³ un regalo delante de la puerta de mi habitación: ¡una bicicleta roja preciosa! Mi madre nos preparó un desayuno riquísimo. Después de desayunar, mis hermanos y yo tuvimos⁴ que limpiar toda la casa, así que (therefore) no hubo⁵ más celebración hasta la tarde. A las seis y media (nosotros) hicimos⁶ una barbacoa en el patio de la casa. Todos los invitados trajeron⁷ bebidas y regalos. Vinieron⁸ todos mis amigos, excepto tú, ¡qué pena! :-( La fiesta estuvo⁹ muy animada hasta las diez de la noche, cuando mis padres dijeron¹⁰ que los vecinos (neighbors) iban a (were going to) protestar y entonces todos se fueron a sus casas.
(1)pudiste¹
(2)dieron²
(3)dejaron³
(4)tuvimos⁴
(5)hubo⁵
(6)hicimos⁶
(7)trajeron⁷
(8)Vinieron⁸
(9)estuvo⁹
(10)dijeron¹⁰
Translation
Hi, Omar: Since you could not come to my birthday party, I want to tell you how it was. On my birthday, very early in the morning, my brothers gave me a big surprise: they left a gift in front of my room door: a beautiful red bicycle! My mother prepared us a delicious breakfast. After breakfast, my brothers and I had to clean the entire house, therefore there was no more celebration until the afternoon. At six thirty we made a barbecue in the yard of the house. All the guests brought drinks and gifts. They came all my friends, except you, what a pity! . The party was very animated until ten at night, when my parents said that the neighbors were going to complain and then everyone went home.