Calculus III: Three Dimensional Vectors (Level 3 of 3)

The video tutorial covers 3D vectors through four examples. It starts with an introduction to 3D vectors, followed by examples of vectors in the YZ and XZ planes, demonstrating how to sketch vectors and find their component forms. The tutorial then explores finding a point two-thirds of the way between two points using vectors. Finally, it addresses a static equilibrium problem, calculating tension forces in a 3D space. The video concludes with a preview of the next series on the dot product.

What is the component form of a vector lying in the YZ plane with a magnitude of 2 and making a 30-degree angle with the positive Y-axis?

• (0, 1, √3)

• (√3, 0, 1)

• (1, 0, √3)

• (0, √3, ±1)

In the second example, what is the angle made by the second vector with the X-axis?

• 135 degrees

• 180 degrees

• 45 degrees

• 90 degrees

What is the magnitude of the vector in the XZ plane with a 45-degree angle to the Z-axis?

• 6

• 5

• 4

• 3

How do you find the point that is two-thirds of the way from Point P to Point Q?

• By subtracting two-thirds of the vector PQ from Point Q

• By dividing the vector PQ by two

• By multiplying the vector PQ by three

• By adding two-thirds of the vector PQ to Point P

In the static equilibrium problem, what is the weight of the crate?

• 600 newtons

• 500 newtons

• 400 newtons

• 300 newtons

What principle is used to solve the static equilibrium problem?

• The sum of all forces equals zero

• Newton's Second Law

• Newton's First Law

• The sum of all torques equals zero

How are the tension forces in the cables expressed in the static equilibrium problem?

• As angles

• As scalars

• As vectors with unknown magnitudes

• As vectors with known magnitudes