Finding the angle between 2 vectors given vectors as linear combinations with angles

The video tutorial covers different methods to represent vectors, including component form, linear combination, and unit vector with magnitude. It explains how to find the angle between two vectors using the cosine formula and demonstrates the calculation of dot products and magnitudes. The tutorial concludes with solving for the angle using inverse cosine, emphasizing the use of unit vectors and the unit circle.

Which of the following is NOT a way to represent a vector?

• Unit vector with magnitude

• Scalar multiplication

• Linear combination

• Component form

Which representation of a vector involves using cosine and sine functions?

• Scalar multiplication

• Unit vector with magnitude

• Linear combination

• Component form

What is the formula to find the angle between two vectors U and V?

• cos(Theta) = (U + V) / (magnitude of U * magnitude of V)

• cos(Theta) = (U dot V) / (U + V)

• cos(Theta) = (U dot V) / (magnitude of U * magnitude of V)

• cos(Theta) = (U cross V) / (magnitude of U * magnitude of V)

What is the dot product of two vectors U and V?

• U1 + V1 + U2 + V2

• U1 / V1 + U2 / V2

• U1 * V1 + U2 * V2

• U1 * V2 + U2 * V1

What is the result of the dot product U dot V if U and V are perpendicular?

• Depends on the vectors

• Infinity

• 0

• 1

What is the magnitude of a unit vector?

• 0

• Depends on the vector

• 1

• Infinity

What is the angle between two identical unit vectors?

• 0 degrees

• 45 degrees

• 90 degrees

• 180 degrees

If the magnitude of a vector is 1, what type of vector is it?

• Unit vector

• Complex vector

• Zero vector

• Scalar vector

How do you calculate the angle using the inverse cosine function?

• Theta = tan^-1((U dot V) / (magnitude of U * magnitude of V))

• Theta = cos^-1((U cross V) / (magnitude of U * magnitude of V))

• Theta = sin^-1((U dot V) / (magnitude of U * magnitude of V))

• Theta = cos^-1((U dot V) / (magnitude of U * magnitude of V))

What is the angle between two vectors if their dot product is negative?

• Less than 90 degrees

• Exactly 90 degrees

• Exactly 180 degrees

• Greater than 90 degrees