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Let a b c be three non zero vectors .if a.(b×c)=0 and b and c are not parallel..then prove a =mb +nc where m and n are some scalars.

Let a b c be three non zero vectors .if a.(b×c)=0 and b and c are not parallel..then prove a =mb +nc where m and n are some scalars.

Grade:12

1 Answers

Deepak Kumar Shringi
askIITians Faculty 4405 Points
3 years ago
here scalar triple product of three vectors is zero(where b &c are not parallel) this represents that a,b,c are lying in the same plane .Now if three vectors are in same plane then any one of them can be written in the form of other two (called linearly dependent vectors) it can be easily proved by linear dependecy of two vectors

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