JEE Advanced2024MathematicsVector AlgebraActual

Let p =2 i + j +3 k and q = i - j + k . If for some real numbers , , and , we have 15 i +10 j +6 k = (2 p + q )+ ( p -2 q )+ ( p q ) then the value of is

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15 i +10 j +6 k = (2 p + q )+ ( p -2 q )+ ( p q ) taking dot with ( p q ) | array ccc 15 & 10 & 6 2 & 1 & 3 1 & -1 & 1 array |=0+0+ ( p ^2 q ^2-( p q )^2 ) [ ( p q )^2+( p q )^2= p ^2 q ^2 ] aligned & 52=26 & =2 aligned

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