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Mathematics
Mathematics
Problem
12. Let
a
⃗
=
i
^
+
4
j
^
+
2
k
^
,
b
⃗
=
3
i
^
−
2
j
^
+
7
k
^
\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}
a
=
i
^
+
4
j
^
+
2
k
^
,
b
=
3
i
^
−
2
j
^
+
7
k
^
and
c
⃗
=
2
i
^
−
j
^
+
4
k
^
\vec{c}=2 \hat{i}-\hat{j}+4 \hat{k}
c
=
2
i
^
−
j
^
+
4
k
^
. Find a vector
d
⃗
\vec{d}
d
which is perpendicular to both
a
⃗
\vec{a}
a
and
b
⃗
\vec{b}
b
, and
c
⃗
⋅
d
⃗
=
15
\vec{c} \cdot \vec{d}=15
c
⋅
d
=
15
.
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