find the cross product of a=2î and b=-2î+4j
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Step-by-step explanation:
The cross product of 2 vectors is calculated with the determinant
∣
∣
∣
∣
∣
→
i
→
j
→
k
d
e
f
g
h
i
∣
∣
∣
∣
∣
where
→
a
=
⟨
d
,
e
,
f
⟩
and
→
b
=
⟨
g
,
h
,
i
⟩
are the 2 vectors
Here, we have
→
a
=
⟨
2
,
−
3
,
4
⟩
and
→
b
=
⟨
1
,
1
,
−
7
⟩
Therefore,
∣
∣
∣
∣
∣
→
i
→
j
→
k
2
−
3
4
1
1
−
7
∣
∣
∣
∣
∣
=
→
i
∣
∣
∣
−
3
4
1
−
7
∣
∣
∣
−
→
j
∣
∣
∣
2
4
1
−
7
∣
∣
∣
+
→
k
∣
∣
∣
2
−
3
1
1
∣
∣
∣
=
→
i
(
(
−
3
)
⋅
(
−
7
)
−
(
4
)
⋅
(
1
)
)
−
→
j
(
(
2
)
⋅
(
−
7
)
−
(
4
)
⋅
(
1
)
)
+
→
k
(
(
2
)
⋅
(
1
)
−
(
−
3
)
⋅
(
1
)
)
=
⟨
17
,
18
,
5
⟩
=
→
c
Verification by doing 2 dot products
⟨
17
,
18
,
5
⟩
.
⟨
2
,
−
3
,
4
⟩
=
(
17
)
⋅
(
2
)
+
(
18
)
⋅
(
−
3
)
+
(
5
)
⋅
(
4
)
=
0
⟨
17
,
18
,
5
⟩
.
⟨
1
,
1
,
−
7
⟩
=
(
17
)
⋅
(
1
)
+
(
18
)
⋅
(
1
)
+
(
5
)
⋅
(
−
7
)
=
0
So,
→
c
is perpendicular to
→
a
and
→
b
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