Vector Calculations and Trigonometric Functions

The video tutorial explains how to find the magnitude and direction angle of a vector with given horizontal and vertical components. It covers the conversion of linear combination to component form, calculating the magnitude using the Pythagorean theorem, and determining the direction angle using the tangent ratio. The final result is presented in trigonometric form, with a magnitude of six radical two and a direction angle of 315 degrees.

What are the horizontal and vertical components of the vector discussed in the video?

• 5 and 5

• 6 and 6

• 5 and -5

• 6 and -6

What is the term used to describe the form where vectors are expressed with sine and cosine values?

• Cartesian form

• Linear form

• Polar form

• Trig form

What is the first step in solving vector problems according to the video?

• Use a calculator

• Find direction angle

• Draw a picture

• Calculate magnitude

How is the linear combination form related to the component form?

• They are unrelated

• They are the same

• Linear form uses i and j

• Component form uses i and j

What mathematical theorem is used to calculate the magnitude of the vector?

• Tangent rule

• Cosine rule

• Sine rule

• Pythagorean theorem

What is the magnitude of the vector as calculated in the video?

• 72

• 12

• 6√2

• 6

What is the perfect square factor of 72 used in the magnitude calculation?

• 18

• 36

• 12

• 6

Which trigonometric function is used to find the direction angle?

• Tangent

• Secant

• Cosine

• Sine

What is the value of the tangent of the angle in the video?

• 2

• 0

• -1

• 1

What is the initial angle found using the inverse tangent function?

• 0 degrees

• 90 degrees

• -45 degrees

• 45 degrees