Chapter 6 - Vectors 1

Question 1

What is the vector equation?

Answer 1

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.

Question 2

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

Answer 2

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

Question 3

Define the scalar/dot product of a vector.

Answer 3

Question 4

What is the dot product of two vectors?

Answer 4

Question 5

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

Answer 5

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)

Question 6

What is the cartesian equation of a line?

Answer 6