Vector Algebra Practice Questions

Here's a set of questions covering various aspects of Vector Algebra:

https://effectuall.github.io/Simulations/Mechanics_Vector_Display.html

1. Vector Basics

• Define a vector and explain how it differs from a scalar quantity.
• What is the magnitude of a vector? How is it calculated in three-dimensional space?
• Explain the concept of a unit vector. How can you convert any vector into a unit vector?

2. Vector Operations

• Describe the process of vector addition using both algebraic and geometric methods.
• How is scalar multiplication of a vector performed? What effect does it have on the vector's magnitude and direction?
• Calculate the dot product of vectors a = 2i + 3j + k and b = i - 2j + 4k. What does the result represent?

3. Vector Algebra in 3D Space

• Given vectors u = 3i - 2j + k and v = i + 4j - 2k, find their cross product. What geometric interpretation does this result have?
• Determine if vectors a = 2i + j - 3k and b = -4i - 2j + 6k are parallel, perpendicular, or neither.
• Find the angle between vectors p = 2i + 2j + k and q = i - j + 2k.

https://effectuall.github.io/Simulations/Mechanics_Vector_Algebra

4. Applications of Vector Algebra

• How can vector algebra be used to find the area of a parallelogram?
• Explain how vector algebra is applied in calculating torque in physics.
• Describe a real-world scenario where vector decomposition is useful.