Cross Product (Outer Product, 3D only)
Formula: a × b = c. Magnitude: |c| = |a| |b| sinθ, where θ is the angle between a and b. Direction: c is perpendicular to the plane containing a and b, determi…
Syllabus path: Geometry and Algebra › Vectors and Complex Numbers › Vector Operations
CSCA Exam Prep
This formula is aligned to the CSCA undergraduate admissions exam syllabus. Continue with the linked tutorial and topic practice.
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CSCA Mathematics Formula Reference
Formula and explanation
Formula: a × b = c. Magnitude: |c| = |a| |b| sinθ, where θ is the angle between a and b. Direction: c is perpendicular to the plane containing a and b, determined by the right - hand rule. Coordinate form (3D): If a = (a₁, a₂, a₃), b = (b₁, b₂, b₃), then a × b = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁). Description: The cross product results in a vector. Its magnitude equals the area of the parallelogram with sides a and b. Applicable Conditions: Only applicable to vectors in three - dimensional space.
Related tutorial and examples
Vector Operations
Vector Operations Vector operations are not just calculation tools but core methods for solving geometric problems. In the CSCA exam, the focus is on coordinate calculations and the conditions for parallelism and perpendicularity. 1. Basic Concepts Definition: A quantity with bot…
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