A plane bisects the line segment joining the points (1, 2, 3) and ($$-$$ 3, 4, 5) at rigt angles. Then this plane also passes through the point :

If the position vectors of the vertices A, B and C of a $$\Delta $$ ABC are respectively $$4\widehat i + 7\widehat j + 8\widehat k,$$    $$2\widehat i + 3\widehat j + 4\widehat k,$$ and $$2\widehat i + 5\widehat j + 7\widehat k,$$ then the position vectors of the point, where the bisector of $$\angle $$A meets BC is :

If the mean of the data : 7, 8, 9, 7, 8, 7, $$\lambda $$, 8 is 8, then the variance of this data is :

A tower T₁ of height 60 m is located exactly opposite to a tower T₂ of height 80 m on a straight road. Fromthe top of T₁, if the angle of depression of the foot of T₂ is twice the angle of elevation of the top of T₂, then the width (in m) of the road between the feetof the towers T₁ and T₂ is :