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Let (hatp xx vecq) xx (hatp.vecq)vecq =(x^(2)+y^(2))vecq + (14-4x-6y)vecp Where hatp and hatq are two non-collinear vectors vecp is unit vector and x,y are scalars. Then the value of (x+y) is

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Solution :`(vecp xx vecq) xx HATP+(hatp.vecc)vecq=(X^(2)+y^(2))vecq+(14-4x-6y)hatp`
`rArr (hatp.hatp)vecq+(1-4x-6y)hatp`
Since `hatp` and `vecq` are non-zero non-collinear.
We can COMPARE coefficients of vectors `hatp` and `hatq`.
`therefore 1+hatp.vecq=x^(2)+y^(2)`.............(i)
And `hatp.vecq=4x+6y-14`............(II)
From (i) and (ii), we get
`rArr x^(2) + y^(2)-4x-6y+13=0`
`rArr (x-2)^(2)+(y-3)^(2)=0`
x=2 and y=3


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