Let's review....
Practice Problem 1:
Given vector a, where the magnitude is 3 in. and the
direction is 70o... and vector b, where the magnitude is 4.3 in.
and the direction is 20o. Find the ordered pair for a + b and its
direction.
Practice Problem 2:
Given vector c, where the magnitude is 7 in. and the
direction is -40o... and vector d, where the magnitude is
7.3 in. and the direction is 30o. Find the ordered pair for
2c-d and its direction
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8.2 Algebraic Vectors
Angled brackets indicate horizontal/vertical components.
- you are given (or create) one set
indicate coordinates.
Rounded brackets
- you are given two sets
- to get the components, subtract!
(x2, y2) - (x1, y1)
Ex. 1: Find the magnitude of YZ. Then find the ordered pair that represents YZ.
Y(2, ­5), Z(3, ­8)
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Ex. 2: Given vector m = 2, ­3 and vector n = 4, 1
Find m + n = Find m ­ n = Find 3m + 2n = 2
8.3 Vectors in Three Dimensional Space
Unit Vector is a vector that has a magnitude of one unit
(remember magnitude = distance)
j
i
Any vector can be expressed as a sum of unit vectors.
then a = 2i + 1j
If a = 2,1
Example 3: For A (2, -7) and B (-1, 5)
Write AB as an ordered pair.
Write AB as the sum of unit vectors.
Find the magnitude of AB.
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Example 4 Write AB as the sum of unit vectors for
A(4, -1) and B (6, 2)
8.3 Three Dimensional Vectors
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z
y
x
In three-dimensional space, we use an
ordered triple (x1, y1, z1) to represent a point.
Example 5 Locate the point at (3, 4, 2) using
the graph above.
Then, Draw the vector from the
origin to that point.
z
Example 6 Locate the point
(3, -2, -1) on the graph.
Then, draw the vector
from the origin to that
point.
(3, -2, -1)
y
x
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Example 7 Write the ordered pair that represents the
vector from A(2, 5) to B(-3, 7), then find its
magnitude.
Example 8 Write the ordered triple that represents the
vector from M(4, 5, -2) to N(9, 3, -4), then
find its magnitude.
Example 9 Find an ordered triple that represents 4v + u
if v = (1, 7, 1) and u = (-4, -2, -6).
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Ex. 10
Write GH as the sum of unit vectors for
G(-2, -5, 4) and H(1, 5, 3).
j
i
k
i
j
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