PreCalc Aim 73­ Unit Vectors.notebook
March 28, 2017
Aim #73: How can we find unit vectors and express vectors in "ij"
notation?
HW: P. 418 # 28, 32, 36, 38, 41, 48; Quiz Thurs., on Aims 70-74
Kickoff: Using the vectors u = <-1,1> and v = <3,1>, find 3u + 2v
graphically. Verify your solution algebraically as well.
Mar 20­2:17 PM
Think About It...
How many possible vectors can you find in one
given direction?
How many possible vectors can you find in one given direction that
have a magnitude of 1?
A unit vector is a vector that has the same direction of a vector v
and a magnitude of 1.
To find a unit vector in the same direction as a given vector v,
divide v by its magnitude.
Mar 21­11:18 AM
1
PreCalc Aim 73­ Unit Vectors.notebook
March 28, 2017
Find a unit vector in the direction of v = <-3, 5>. Then verify that the
resulting vector has a magnitude of 1.
Find a unit vector in the direction of v = <5, -12>. Then verify that the
resulting vector has a magnitude of 1.
Mar 20­2:18 PM
To find a vector of a desired magnitude in the same direction as a
given vector v, divide v by its magnitude then multiply by the desired
magnitude.
Find a vector of magnitude 5 in the direction of v = <3, 3>. Then verify
that the resulting vector has a magnitude of 5.
Find a vector of magnitude 9 in the direction of v = <2, 5>. Then verify
that the resulting vector has a magnitude of 9.
Mar 20­2:19 PM
2
PreCalc Aim 73­ Unit Vectors.notebook
March 28, 2017
The unit vectors <1,0> and <0,1> are called the standard unit vectors
and are denoted by i = <1,0> and j = <0,1>,
Any vector in he plane can be written as a linear combination of
standard unit vectors in the form v1i + v2j
Example: <-2, 4> can be rewritten as
-2<1,0> + 4<0,1>
or
-2i + 4j
Try: Rewrite <-9, -3> in ij form.
Try: If vector v has initial point P=(3,2) and terminal point Q=(5,7),,
write v in ij form.
Mar 20­2:19 PM
Let u = -3i + 8j and v = 2i - j. Determine the following:
a) u + v
b) u - v
c) ||v||
d) ||u + v||
e)2u + 3v
f) 5v - u
Mar 21­11:36 AM
3
PreCalc Aim 73­ Unit Vectors.notebook
March 28, 2017
Find the vector v, in ij form, with magnitude 3 in the same
direction as u = 3i + 2j.
Mar 20­2:19 PM
4

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