How to find the magnitude and direction of a given vector

The video tutorial explains how to calculate the magnitude and directional angle of a vector. It begins with an introduction to directional angles and linear combinations, followed by a detailed explanation of how to calculate the magnitude of a vector using its components. The tutorial then covers the simplification of square roots involved in the magnitude calculation. Finally, it demonstrates how to find the directional angle using the tangent function and its inverse, providing both negative and positive angle interpretations.

What is the linear combination of a vector V in terms of trigonometric functions?

• V = cos(Theta) * I + sin(Theta) * J

• V = sec(Theta) * I + csc(Theta) * J

• V = sin(Theta) * I + cos(Theta) * J

• V = tan(Theta) * I + cot(Theta) * J

How do you calculate the magnitude of a vector V with components V1 and V2?

• V1^2 - V2^2

• V1 * V2

• sqrt(V1^2 + V2^2)

• V1 + V2

Which of the following is a correct simplification of sqrt(72)?

• 6 * sqrt(3)

• 6 * sqrt(2)

• 3 * sqrt(4)

• 4 * sqrt(2)

What is the directional angle if tan(Theta) equals -1?

• 90 degrees

• -45 degrees

• 315 degrees

• 45 degrees

How do you convert a negative angle to its positive equivalent on a circle?

• Subtract 360 degrees

• Add 360 degrees

• Subtract 90 degrees

• Add 90 degrees