Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

If a , b , c be three non zero vectors satisfying the condition a b = c & b c = a then which of the following always hold(s) good?

Options

Aa , b , c are orthogonal in pairs
B[ a b c ]=| b |
C[ a b c ]=| c |^2
D| b |=| c |

Correct answer

C. [ a b c ]=| c |^2

Step-by-step solution

Clearly a c =0 and b c =0 Also a b =0 A a b = c dot with b b c =0 Similarly b c = a dot with b a b =0 ; dot with c a c =0 a b = b c = c a =0 Again aligned & | a | b |=| c | & | b || c |=| a | aligned | a | | c | = | c | | a | | a |=| c | &| b |=1 a b c =| a || b || c |=| a |^2=| c |^2

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