AP EAMCET202422 May 2024Morning ShiftMathematicsVector AlgebraActual

If is the angle between f = i +2 j -3 k and g =2 i -3 j +a k and = 24 28 then 7 a^2+24 a=

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Correct answer

A. 10

Step-by-step solution

aligned & f = i +2 j -3 k , g =2 i -3 j +a k & | f g |=| f || g | ....(i) aligned Now, f g = | array ccc i & j & k 1 & 2 & -3 2 & -3 & a array |=(2 a-9) i -(a+6) j -7 k aligned & | f g |= (2 a-9)^2+(a+6)^2+49 & = 5 a^2-24 a+166 aligned From (i) we get, aligned & 5 a^2-24 a+166=14 (12+a^2 ) 24 28 & 7 a^2+24 a=10 aligned

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