Explore the fundamentals of multivariable calculus in this comprehensive 90-minute tutorial. Begin with an introduction to vectors in two and three dimensions, learning to calculate vector lengths and perform basic vector operations. Delve into vector addition, scalar multiplication, and subtraction before examining the algebraic properties of vectors. Study the dot product and its applications, including finding angles between vectors and identifying orthogonal vectors. Conclude by mastering vector and parametric equations of lines in three-dimensional space, with practical examples on finding line equations and determining intersection points between lines and planes.