Chapter 2.9 Dot Product

To add two vectors, A and B, using the parallelogram law, they must be first joined as follows: 

The tail of vector A must meet the tail of vector B

A particle has a weight of 306 N, what is its mass in kg? Type your answer with 3 sig figs.

31.2

The coordinate direction angles α, β, γ are determined between a vector and which of the following?

positive z-axis

positive x-axis

positive y-axis

How to determine the angle between 2 vectors

A*B=ABcos(theta)

The dot product operation yields:

a scalar

If A→⋅B→=0 , this signifies that the vectors A→ and B→ are:

perpendicular

Parallel Formula

Scalar form: A||=A*U

Vector form: A||=A||U

Perpendicular formula

Scalar form: A-=Sqrt(A²-A²||)

Vector form: A-=A-A||

In Examples 2.15 and 2.16 of your textbook, the unit vector of a line is determined such that the dot product can be utilized to find the projection of the given vector along this same line. How is the unit vector determined?

The position vector is used to determine the unit vector of the line

Dot Product is used when…

You are given a set of plots with a force starting from point o and you are being asked to find the angle between the 2 points.

If a question asks to find the component parallel and perpendicular to a segment or (position vector)

Always find unit vectors for both components

Use Dot product for parallel

Use Pythagorean looking equation to find perpendicular

When looking for Angle between two vectors

Always find unit vectors for both components

Use Dot product for parallel component

Use Theta=acos(parallel component)