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Engineering

If a point P( $\alpha, \beta, \gamma$ ) satisfying $(\alpha \beta \gamma) \begin{pmatrix} 1 & 10 & 8 \\ 9 & 3 & 8 \\ 8 & 4 & 8 \end{pmatrix} = (0 0 0)$ lies on the plane $2x + 4y + 3z = 5$ , then $6\alpha + 9\beta + 7\gamma$ is equal to :

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A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is: [Diagram: Semicircular arc with mass m at center]

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