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JEE Main202522 Jan 2025Morning ShiftMathematicsVector AlgebraActual

Let c be the projection vector of b = i +4 k , 0 , on the vector a = i +2 j +2 k . If | a + c |=7 , then the area of the parallelogram formed by the vectors b and c is ________

Correct answer

0

Step-by-step solution

c = ( b a | b | ) a | a | aligned & = ( +8 9 )( i +2 j +2 k ) & | a + c |=7 & . ( +8 9 +1 ) i + ( 2( +8) 9 +2 ) j + ( 2( +8) 9 +2 ) k ,=7 & ( +8 9 +1 )^2+ ( 2( +8) 9 +2 )^2+ ( 2( +8) 9 +2 )^2=49 aligned =4 c = 4 3 i + 8 3 j + 8 3 k Area of parallelogram = | array ccc i & j & k 4 3 & 8 3 & 8 3 4 & 0 & 4 array |=16

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