Vector Analysis and Trigonometry Concepts

The video tutorial explains how to analyze and combine two vectors, A and B, by decomposing them into horizontal and vertical components. It uses trigonometric properties of 30-60-90 and 45-45-90 triangles to determine the components of each vector. The tutorial then combines these components to find the resultant vector A plus B, providing a detailed step-by-step approach to vector addition.

What is the magnitude of vector A?

• 2

• 5

• 3

• 4

At what angle does vector B form with the positive x-axis?

• 180 degrees

• 135 degrees

• 90 degrees

• 45 degrees

What is the purpose of decomposing vectors into components?

• To change their direction

• To make them perpendicular

• To increase their magnitude

• To simplify calculations

Which unit vector represents the horizontal component?

• I

• J

• K

• L

In a 30-60-90 triangle, what is the length of the side opposite the 30-degree angle if the hypotenuse is 3?

• 3

• 2.5

• 2

• 1.5

What is the cosine of a 30-degree angle?

• √3/2

• 1/2

• 1

• √2/2

In a 45-45-90 triangle, what is the sine of a 45-degree angle?

• 1

• 1/2

• √3/2

• √2/2

What is the length of the horizontal component of vector B?

• -2√2

• 2√2

• -√2

• √2

How do you find the resultant vector A + B?

• By subtracting the components

• By adding the components

• By multiplying the components

• By dividing the components

What is the vertical component of vector A?

• √3/2

• 3/2

• √2

• 3√3/2