Let $$OA$$ $$CB$$ be a parallelogram with $$O$$ at the origin and $$OC$$ a diagonal. Let $$D$$ be the midpoint of $$OA.$$ Using vector methods prove that $$BD$$ and $$CO$$ intersect in the same ratio. Determine this ratio.

In the formula X = 3YZ², X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are _____________

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

Two bodies M and N of equal masses are suspended from two separate massless springs of spring constant k₁ and k₂ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of M to that of N is