Understanding Resultant Vectors

This video tutorial explains how to calculate the magnitude and direction of a resultant vector formed by the sum of two force vectors. It covers breaking down each vector into its x and y components, using trigonometric functions to find these components, and then summing them to get the resultant vector. The tutorial also demonstrates how to graph the vector and calculate its magnitude using the Pythagorean theorem, as well as how to determine its direction using the arc tangent function.

What is the first step in finding the resultant vector of two force vectors?

• Multiply the magnitudes of the vectors

• Add the vectors directly

• Subtract the vectors

• Break down each vector into its component form

How do you calculate the x component of a force vector?

• Add the force to the angle

• Divide the force by cosine of the angle

• Multiply the force by cosine of the angle

• Multiply the force by sine of the angle

What is the value of cosine 30 degrees used in the calculation of f1x?

• 0.866

• 0.707

• 1.0

• 0.5

What is a unit vector?

• A vector with a magnitude of two

• A vector with a magnitude of three

• A vector with a magnitude of one

• A vector with a magnitude of zero

Why is the x component of f2 negative?

• Because it is in the first quadrant

• Because it is in the second quadrant

• Because it is in the third quadrant

• Because it is in the fourth quadrant

What is the angle relative to the positive x-axis for f2?

• 90 degrees

• 45 degrees

• 135 degrees

• 180 degrees

How do you find the resultant vector in component form?

• By dividing the components of f1 and f2

• By multiplying the components of f1 and f2

• By adding the components of f1 and f2

• By subtracting the components of f1 and f2

What formula is used to calculate the magnitude of the resultant vector?

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 / b^2 = c^2

• a^2 * b^2 = c^2

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

• 212.1 newtons

• 173.2 newtons

• 314.5 newtons

• 100 newtons

What is the direction of the resultant vector relative to the positive x-axis?

• 135 degrees

• 97.1 degrees

• 82.9 degrees

• 45 degrees