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Mathematics
Mathematics
Problem
Let
a
⃗
=
x
i
+
3
j
+
4
k
\vec a = x\mathbf i + 3\mathbf j + 4\mathbf k
a
=
x
i
+
3
j
+
4
k
, where
x
x
x
is a real number, and let
b
⃗
=
2
i
−
j
+
k
\vec b = 2\mathbf i - \mathbf j + \mathbf k
b
=
2
i
−
j
+
k
. a. (i) If
∣
a
⃗
×
b
⃗
∣
=
10
3
\bigl|\vec a \times \vec b\bigr| = 10\sqrt{3}
a
×
b
=
10
3
, determine all possible values of
x
x
x
. b. (ii) For each value of
x
x
x
found in part (i), find every unit vector that is perpendicular to both
a
⃗
\vec a
a
and
b
⃗
\vec b
b
.
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