You are given a parallelogram ABCD. Points E and N are the midpoints of sides BC and CD, respectively.

univerkov | August 12, 2021 | education

You are given a parallelogram ABCD. Points E and N are the midpoints of sides BC and CD, respectively. Express the vectors AE and AN in terms of the vectors AB = a and AD = b.

Opposite sides of a parallelogram are equal and parallel.

Points E and N are the middle of the sides BC and CD, then BE = CE = BC / 2, CN = DN = CD / 2.

Then the vector ↑ BE = ↑ BC / 2 = ↑ AD / 2 = ↑ b / 2, vector ↑ DN = ↑ DC / 2 = ↑ AB / 2 = ↑ a / 2.

Vector ↑ AE = ↑ AB + BE = ↑ a + ↑ b / 2.

Vector ↑ АN = ↑ АD + DN = ↑ b + ↑ a / 2.

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