Vectors and Basic Operations

Vectors and Basic Operations in Math Linear Algebra brings together interactive vector calculators that cover the core skills of vector arithmetic in 2D and 3D, including vector addition and subtraction, scalar multiplication, dot product, cross product, and vector norm and distance calculations.

The chapter supports beginners building fundamentals (components, magnitude, direction, and clean vector notation) while also extending into more advanced linear algebra topics like vector projection, orthogonalization ideas, and Gram–Schmidt orthogonalization for constructing orthonormal sets.

Students, teachers, and self-learners can use these tools to check homework, practice for exams, and confirm results with step-by-step outputs that reduce sign and component errors—especially when working with angles, distances, projections, and orthogonality. It’s also useful for advanced users who want fast, accurate verification for applications in physics and engineering vectors, geometry, computer graphics, and data science workflows.