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If a, b are non collinear vectors and r+r Cross a=b then r=

If a, b are non collinear vectors 
and r+r Cross a=b then r=

Grade:12th pass

1 Answers

Aditya Gupta
2080 Points
2 years ago
the first thing to be said about this ques is that it is really hard and uses several principles. to solve the ques, take 
r= xa+yb+z(axb) …. the reason why we can do this is coz a, b and a cross b are LINEARLY INDEPENDENT. 
now plug in this value of r in the given eqn, and then you will have to use gthe formula for vector triple product which says:
ax(bxc)= (a.c)b – (a.b)c
after doing all of this, you will get an eqn of the form
ea+fb+g(axb)=0 where e f and g are expressions in x y and z.
but due to linear independence, e=f=g=0
so solving these 3 eqns in e variables x y and z you will get
y=z=1/(1+|a|^2)
and x= (a.b)/(1+|a|^2)
hence, r= xa+yb+z(axb) has been correctly determined!

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