Vector Calculations and Angle Determination

The video tutorial explains how to use the cosine formula to find the angle between two vectors. It covers calculating the magnitude of vectors using the Pythagorean theorem and provides examples with specific vectors. The process involves finding the dot product of the vectors, dividing by their magnitudes, and using the cosine inverse to determine the angle.

What is the formula used to find the angle between two vectors?

• Tangent Theta equals u.v divided by magnitudes

• Cosine Theta equals u.v divided by magnitudes

• Secant Theta equals u.v divided by magnitudes

• Sine Theta equals u.v divided by magnitudes

What does the magnitude of a vector represent?

• The speed of the vector

• The length of the vector

• The angle of the vector

• The direction of the vector

How do you calculate the magnitude of a vector with coordinates (x, y)?

• Add x and y

• Multiply x and y

• Square root of (x^2 + y^2)

• Square root of (x + y)

What is the magnitude of a vector with coordinates (3, 4)?

• 3

• 4

• 5

• 7

What is the first step in finding the angle between two vectors?

• Calculate the cross product

• Find the inverse sine

• Dot the two vectors

• Find the magnitudes

What is the dot product of vectors U(3, 4) and V(5, -12)?

• 65

• 15

• -48

• -33

What is the magnitude of vector V with coordinates (5, -12)?

• 5

• 17

• 12

• 13

What operation is used to isolate Theta in the cosine formula?

• Sine inverse

• Cosine inverse

• Tangent inverse

• Secant inverse

What is the result of simplifying the expression -33/65?

• -0.5

• -0.6

• -0.7

• -0.8

What is the final step in finding the angle between two vectors?

• Calculate the cross product

• Find the inverse cosine

• Multiply the magnitudes

• Add the vectors