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What is a unit vector and how is it used?
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A unit vector has a magnitude of one, used to denote direction in components.
Using trigonometry, how can the y-component of a vector be calculated?
f_y = f × sin(θ)
When is it useful to express vectors in component form?
Component form is useful for calculations in multiple dimensions, simplifying vector addition and subtraction.
Differentiate between vectors and scalars using acceleration.
Acceleration is a vector because it describes how velocity changes with direction, not just how quickly.
What does the Pythagorean theorem state about vectors?
The theorem states that the magnitude of a vector is calculated as √(f_x² + f_y²).
What is the relationship between velocity and speed?
Velocity includes both speed and direction; speed is only the magnitude.
How does displacement differ from distance?
Displacement includes direction whereas distance does not.
Explain SOHCAHTOA in the context of vector components.
It's a mnemonic to remember the sine, cosine, and tangent ratios for right triangles.
Define scalar quantity with examples.
Scalars have only magnitude, examples include temperature and mass.
Express a vector with components f_x = 86.6 and f_y = 50 using unit vectors.
f = 86.6i + 50j
Calculate the x-component of a force vector 100 N at 30° above x-axis.
f_x = 100 × cos(30°) = 86.6 N
Why is force considered a vector quantity?
Force has both magnitude and direction.
How do you determine the magnitude of a vector from its components?
Using the Pythagorean theorem: magnitude = √(f_x² + f_y²)
Explain how trigonometric functions are used to find vector angles.
Trigonometric functions like sine, cosine, and tangent relate the angles to the sides of right triangles.
What defines a vector quantity?
A vector quantity has both magnitude and direction.
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