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Vectors

Blazing goIITian

Joined:	31 Jan 2007
Post:	515

7 Apr 2008 20:38:06 IST

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342

orthogonal vectors-rates assured!!!!!!!!!!

None

a,b,c are non-coplanar vectors and

b1=b-a(b.a/|a|^2 )

b2=b + a(b.a/|a|^2 )

c1=c-a(c.a/|a|^2 ) + b1(b.c/|c|^2)

c2=c-a(c.a/|a|^2 ) - b1(b.c/|b1|^2)

c3=c-a(c.a/|c|^2 ) + b1(b.c/|c|^2)

c4=c-a(c.a/|c|^2 ) - b1(b.c/|b1|^2)

then the set of orthogonal vectors is

1) (a,b1,c3)

2) (a,b1,c2)

3) (a,b2,c2)

4) (a,b1,c1)

ans is 2).plz xplain how.

rates assured

!!!!!!!!!!!!!

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Comments (1)

ram kumar

Blazing goIITian

Joined: 14 Aug 2007

Posts: 407

7 Apr 2008 20:50:50 IST

Like 2 people liked this

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

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

$a.b_1\;=\;a.b-b.a\;=\;0$ .........(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??????

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