The video tutorial explains the analytical method of vector addition and subtraction. It begins with vectors A and B in the x-y plane, detailing their components and how to sum them. The commutative property of vectors is highlighted, allowing rearrangement of terms. The tutorial extends the concept to three dimensions, showing how to add vectors A and B with components in the x, y, and z directions. Finally, it demonstrates adding and subtracting multiple vectors, using vectors A, B, and C to illustrate the process.

What is the result of adding two vectors A and B in the x-y plane?

• A vector with components Ax * Bx and Ay * By

• A vector with components Ax - Bx and Ay - By

• A vector with components Ax + Bx and Ay + By

• A vector with components Ax / Bx and Ay / By

In three-dimensional space, what is the z-component of the resultant vector R when adding vectors A and B?

• Az + Bz

• Az - Bz

• Az * Bz

• Az / Bz

How do you calculate the x-component of vector T, which is the result of A + B - C?

• Ax - Bx - Cx

• Ax + Bx - Cx

• Ax - Bx + Cx

• Ax + Bx + Cx

What is the y-component of vector T when T = A + B - C?

• Ay + By + Cy

• Ay - By + Cy

• Ay + By - Cy

• Ay - By - Cy

Which of the following correctly represents the z-component of vector T?

• Az - Bz - Cz

• Az + Bz - Cz

• Az - Bz + Cz

• Az + Bz + Cz