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Example 1:
Example 2
Vector A =
3
0
Vector B =
0
3
o
theta
=
90
A.B = |A| |B| cos theta
=
|A| |B| cos 90
=
|A| x |B| x 0
=
0
..
. A.B = 0,
Vector A is perpendicular to Vector B
Vector A =
1
4
A
Vector B =
5
?
B
2
theta
=
?
A.B
=
|A| |B| cos theta
2
2
2
2
(1x5)+(2x4)
=
1 + 4
x
5
+
2
x
cos theta
5
+
8
=
17
x
29
x
cos theta
13
=
17
x
29 x
cos theta
13
17
x
29
=
cos theta
0.585
=
cos theta
theta
= cos
-1
(0.585)
o
theta
=
54.2
Two
Dimensiona
l
Three Dimensional
u.v = (u
x
x
v
x
) + ( u
y
x
v
y
)
u.v = (u
x
x v
x
) + ( u
y
x v
y
)
+
(u
z
x
v
z
)
To find theta:
?
=
cos
-1
((u.v) / (|u||v|))
Example:
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