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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

If [ b c d ]=48 and ( a b ) ( c d )+( a c ) ( d b )+( a d ) ( b c )+k a = 0 (where a is a non zero vector), then find value of k .

Correct answer

96

Step-by-step solution

aligned & T₁=( a b ) ( c d ) & T₂=( a c ) ( d b ) & T₃=( a d ) ( b c ) aligned Then, aligned & T₁= [ array lll c & d & a array ] b - [ array lll c & d & b array ] a & T₂= [ array lll d & b & a array ] c - [ array lll d & b & c array ] a & T₃= [ array lll a & d & c array ] b - [ array lll a & d & b array ] c & aligned Sum =-2 [ array lll b & c & d array ] a +k a =0[Given . [ array lll b & c & d ] array ]=48 ] Hence, k=96

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