IIT JEE , AIEEE Forum - Mathematics , Vectors - orthogonal vectors-rates assured!!!!!!!!!!

ramkumar_november

$a.b_1\;=\;a.b-\frac{a.a(b.a)}{|a|^2}$

$a.b_1\;=\;a.b-\frac{|a|^2(b.a)}{|a|^2}$

$a.b_1\;=\;a.b-b.a\;=\;0$ .........(1)

$so\; a \;\;and\;\;b_1\;\;are \;\;orthogonal$

$a.c_2\;=\;a.c-\frac{a.a(c.a)}{|a|^2}+\frac{a.b_1(b.c)}{|b|^2}$

$a.c_2\;=\;a.c-c.a+ 0 \;\;(from \;(1))$

$a.c_2\;=\;0$

$so\;\;a\;\;and\;\;c_2\;\;are\;\; orthogonal$

so the answer is 2...... clear??????