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I a,b,c be three unit vectors such that a*(b*c)=1/2b and b is not parallel to c then the angle between a and c is

I a,b,c be three unit vectors such that a*(b*c)=1/2b and b is not parallel to c then the angle between a and c is

Grade:12

3 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago
Dear pallavi a X(b X c)=1/2b or (a.c)b -(a.b)c =1/2 b or ((a.c) -1/2)b - (a.b)c =0 b is not parallel to c so coefficient of b must be zero a.c -1/2 =0 a.c =1/2 |a| |c| cosT =1/2 where T is angel between a and c 1*1* cosT =1/2 T =60 Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE & AIEEE preparation. All the best. Regards, Askiitians Experts Badiuddin
Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear pallavi

a X(b X c)=1/2b

or (a.c)b -(a.b)c =1/2 b

or ((a.c) -1/2)b - (a.b)c =0

b is not parallel to c so coefficient of b must be zero

a.c -1/2 =0

a.c =1/2

|a| |c| cosT =1/2 where T is angel between a and c

1*1* cosT =1/2

T =60

Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE & AIEEE preparation.

All the best. Regards,

Askiitians Experts

 Badiuddin

ankit singh
askIITians Faculty 614 Points
3 years ago

 a×(b×c)=(a⋅c)b−(a⋅b)c=21​b
⇒(a⋅c−1/2)b=(a⋅b)c
But b and c are non parallel so
a⋅c−1/2=0,a⋅b=0
⇒ angle between a and c is π/3 and the angle between a and b is π/2

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