How to write a vector in three different forms

The video tutorial reviews vector concepts, including component form, magnitude, and angle. It introduces unit vectors, explaining their properties and how to derive them. The tutorial explores different vector forms, such as component and magnitude-direction forms, and explains how to use linear combinations to represent vectors. The session emphasizes understanding vector properties and transformations.

What is the component form of a vector that starts at the origin and ends at the point (4, 3)?

• (0, 0)

• (4, 3)

• (3, 4)

• (4, 0)

How is the magnitude of a vector related to the Pythagorean theorem?

• It is the product of the components.

• It is the difference between the components.

• It is the sum of the components.

• It is the square root of the sum of the squares of the components.

What is the magnitude of a unit vector?

• 0

• 3

• 2

• 1

How do you convert a vector into a unit vector?

• Multiply by its magnitude.

• Divide by its magnitude.

• Subtract its components.

• Add its components.

What is the angle of a vector with components (4, 3) using the tangent formula?

• 60 degrees

• 36.87 degrees

• 30 degrees

• 45 degrees

How can you represent a vector on the unit circle?

• Using its angle and magnitude.

• Using its components only.

• Using its direction only.

• Using its magnitude only.

What happens to a vector when it is multiplied by a scalar?

• Its components are subtracted.

• Its components are added.

• Its direction changes.

• Its magnitude changes.

How do you express a vector as a linear combination of unit vectors?

• Using only the 'i' vector.

• Using neither 'i' nor 'j' vectors.

• Using only the 'j' vector.

• Using both 'i' and 'j' vectors.

What is the role of 'i' and 'j' in vector representation?

• They represent scalar multiples.

• They represent horizontal and vertical unit vectors.

• They represent imaginary numbers.

• They represent angles.

If a vector is expressed as 4i + 3j, what does this indicate?

• 4 units in magnitude and 3 units in direction.

• 4 units diagonally and 3 units diagonally.

• 4 units horizontally and 3 units vertically.

• 4 units vertically and 3 units horizontally.