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If a,b,c be the unit vectors such that b is not parallal to c and a X(2bXc)=b then the angle that a makes with b and c are respectively where (X represents cross product)

If a,b,c be the unit vectors such that b is not parallal to c and a X(2bXc)=b then the angle that a makes with b and c are respectively where (X represents cross product)

Grade:12th pass

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 years ago
We need to look at only one relation
2a\times(b\times c) = b
Taking dot product both sides wrt a the LHS will become zero (obviously)
hence
b.a = 0
also now we can expand the given vector triple product as
2a \times (b \times c) = 2b(a.c) - 2c(a.b) = 2b(a.c) = b
as a.b=0 and equating to RHS
Thus we get
a.c= 1/2
Thus angle between a and b is 90 and angle between a and c is 60

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