ABCDA1B1C1D1 -parallelepiped .D1C meets C1D at point M. Express the vector AM in terms of vectors AD1 and AC.

univerkov | April 29, 2021 | education

We construct additionally the vector D1K parallel to the vector AC and coinciding in direction, and the vector CК parallel to the vector AD1.

Then the vector AK = AD1 + D1K = AD1 + AC.

Quadrangle AD1KС is a parallelogram, since its opposite sides are parallel.

Then, by the property of the parallelogram, its diagonals, at the point of their intersection, are divided in half.

AM = AK / 2.

Then the vector AM = AK / 2 = (AD1 + AC) / 2.

Answer: Vector AM = (AD1 + AC) / 2.

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