Find dot product of A=3i+3k B=3i-2j+1k
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Explanation:
See below.
Explanation:
a
=
3
i
−
2
j
+
k
8888
b
=
−
2
i
+
2
j
+
4
k
The magnitude of a vector
a
with components
x
1
,
x
2
,
x
3
is defined as:
|
|
a
|
|
=
√
(
x
1
)
2
+
(
x
2
)
2
+
(
x
3
)
2
This is just the distance formula found in coordinate geometry.
We can find the angle between two vectors by using the dot product
For vectors
a
and
b
a
⋅
b
=
|
|
a
|
|
⋅
|
|
b
|
|
⋅
cos
(
θ
)
The multiplication is carried out in a different way than multiplying brackets in algebra. We usually multiply brackets in algebra:
(
a
+
b
+
c
)
(
d
+
e
+
f
)
=
a
d
+
a
e
+
a
f
+
b
d
+
b
e
+
b
f
+
c
d
+
c
e
+
c
f
In the dot product we multiply corresponding components and sum the results:
(
a
1
+
b
1
+
c
1
)
(
a
2
+
b
2
+
c
2
)
=
a
1
a
2
+
b
1
b
2
+
c
1
c
2
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