Vector equation of lines (recap)

Find a vector equation of the line through the points ( 2, 5 ) and ( 4, 9).

Find a vector equation of the line parallel to the x-axis through the point ( 6, 3)

Find a vector equation of the line parallel to i - 4j through the origin

Vectors lesson 3

Vectors in 3Di, j, k

Vector equation of a lineIntersection of two lines

Practice questions

Vectors in 3D

The axis below are said to be “right-handed”: if the outstretched index fingerof your right hand points in the x-direction, and you bend your middle fingerto point in the y direction, then your thumb can naturally point up to the z direction

i, j, k

x

y

z

Vector equation of lines (in 3D)

Find a vector equation of the line parallel to the z-axis through the point (3, 4, -7)

Find a vector equation of the line through the points ( 2 ,5 ,7 ) and (1 ,4, 9).

Find a vector equation of the line through i - 5j + 2k parallel to i - 2k

Intersection of lines

Likely in 2-D not likely in 3-D

Skew lines

In 3D lines which do not meet can be parallel or not parallel.

If they do not meet and they are not parallel they are said to be skew lines

Example:Find where the lines r=(j - k) + s(i + 2j + k) and r=(i + 7j - 4k) +t(i + 3k) intersect

Practice qs

Misc Ex 5 pages 70-71 qs 1, 2, 3, 4, 5