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Mathematics
Mathematics
Problem
Let
a
⃗
=
4
i
^
−
j
^
+
3
k
^
\vec{a}=4\hat{i}-\hat{j}+3\hat{k}
a
=
4
i
^
−
j
^
+
3
k
^
,
b
⃗
=
10
i
^
+
2
j
^
−
k
^
\vec{b}=10\hat{i}+2\hat{j}-\hat{k}
b
=
10
i
^
+
2
j
^
−
k
^
and a vector
c
⃗
\vec{c}
c
be such that
2
(
a
⃗
×
b
⃗
)
+
3
(
b
⃗
×
c
⃗
)
=
0
⃗
.
2(\vec{a}\times\vec{b})+3(\vec{b}\times\vec{c})=\vec{0}.
2
(
a
×
b
)
+
3
(
b
×
c
)
=
0
.
If
a
⃗
⋅
c
⃗
=
15
\vec{a}\cdot\vec{c}=15
a
⋅
c
=
15
, then
c
⃗
⋅
(
i
^
+
j
^
−
3
k
^
)
\vec{c}\cdot(\hat{i}+\hat{j}-3\hat{k})
c
⋅
(
i
^
+
j
^
−
3
k
^
)
is equal to:
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