Let the image of the point $$\left(\frac{5}{3}, \frac{5}{3}, \frac{8}{3}\right)$$ in the plane $$x-2 y+z-2=0$$ be P. If the distance of the point $$Q(6,-2, \alpha), \alpha > 0$$, from $$\mathrm{P}$$ is 13 , then $$\alpha$$ is equal to ___________.

Match List - I with List - II

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Which graph represents the difference between total energy and potential energy of a particle executing SHM vs it's distance from mean position ?

A bullet of $$10 \mathrm{~g}$$ leaves the barrel of gun with a velocity of $$600 \mathrm{~m} / \mathrm{s}$$. If the barrel of gun is $$50 \mathrm{~cm}$$ long and mass of gun is $$3 \mathrm{~kg}$$, then value of impulse supplied to the gun will be :