Vault Of Euclid

Area of a Parallelogram in 3D Space

Vector spaces warmup

Find the area of the parallelogram \(PQRS\) with vertices \(P(1, 1, 0), Q(7, 1, 0), R(9, 4, 2),\) and \(S(3, 4, 2).\)

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What you need first

Vector subtraction to find a vector between two points
Computing the cross product of two 3D vectors
Calculating the magnitude of a 3D vector
Simplifying square roots

What this problem tests

Tests the ability to construct vectors from points, compute a cross product, and find its magnitude.

This is a standard introductory problem in multivariable calculus or linear algebra, demonstrating the geometric interpretation of the cross product.

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