why electric lines of force do not intersect each other ?

Reason:-

Tangent at any point on the line of force gives the direction of electric intensity at that point.

I.e

let two electric lines of force intersect each other then their is possibility of two direction of electric lines of force at that point which is not possible because every point have a unique direction of electric field.that is why electric lines of force do not intersect each other.

Look at the figure which give you more clarity about my words

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