If a is any vector then prove that a=(a.i)+(a.j)j+(a.k)k.

Asked by sunil2791 | 21st Nov, 2017, 06:04: PM

Expert Answer:

Let a be the vector such that 
begin mathsize 16px style straight a with rightwards harpoon with barb upwards on top equals straight u straight i with hat on top plus straight v straight j with hat on top plus straight w straight k with hat on top
open parentheses straight a straight i with hat on top close parentheses straight i with hat on top plus open parentheses straight a straight j with hat on top close parentheses straight j with hat on top plus open parentheses straight a straight k with hat on top close parentheses straight k with hat on top
equals open square brackets open parentheses straight u straight i with hat on top plus straight v straight j with hat on top plus straight w straight k with hat on top close parentheses times straight i with hat on top close square brackets plus open square brackets open parentheses straight u straight i with hat on top plus straight v straight j with hat on top plus straight w straight k with hat on top close parentheses times straight j with hat on top close square brackets plus open square brackets open parentheses straight u straight i with hat on top plus straight v straight j with hat on top plus straight w straight k with hat on top close parentheses times straight k with hat on top close square brackets
Using space straight i with hat on top times straight j with hat on top equals straight j with hat on top times straight k with hat on top equals straight k with hat on top times straight i with hat on top equals 0 space and space straight i with hat on top times straight i with hat on top equals straight j with hat on top times straight j with hat on top equals straight k with hat on top times straight k with hat on top equals 1
You space will space get space straight u straight i with hat on top plus straight v straight j with hat on top plus straight w straight k with hat on top space equals space straight a with rightwards harpoon with barb upwards on top end style

Answered by Sneha shidid | 29th Nov, 2017, 11:37: AM