# Chapter 6 - Vectors 1 Flashcards

## Vector Equations of a line, Scalar Product and Finding Distances. It's all about finding your direction...

What is the vector equation?

Where a and b are vectors:

r = a + λb is the vector equation of a line which is parallel to the vector b and which passes through the point with position vector a.

How do you convert an equation of a vector from a parametric equation to a Cartesian equation?

To convert a vector equation from parametric equation to Cartesian equation, you rearrange to make lambda the subject!

Define the scalar/dot product of a vector.

What is the dot product of two vectors?

How do you calculate the shortest distance from a position vector C, from a line r = a + λb

There are two rules in finding the shortest distance from C to D (a perpendicular position on r = a + λb)

the scalar product (c - (a + λb))•b = 0

since DC = c - (a + λb)

What is the cartesian equation of a line?