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Mathematics
Mathematics
Problem
Let
a
⃗
=
i
^
+
2
j
^
+
k
^
\vec{a} = \hat{i} + 2\hat{j} + \hat{k}
a
=
i
^
+
2
j
^
+
k
^
,
b
⃗
=
3
(
i
^
−
j
^
+
k
^
)
\vec{b} = 3(\hat{i} - \hat{j} + \hat{k})
b
=
3
(
i
^
−
j
^
+
k
^
)
. Let
c
⃗
\vec{c}
c
be the vector such that
a
⃗
×
c
⃗
=
b
⃗
\vec{a} \times \vec{c} = \vec{b}
a
×
c
=
b
and
a
⃗
⋅
c
⃗
=
3
\vec{a} \cdot \vec{c} = 3
a
⋅
c
=
3
. Then
a
⃗
⋅
(
(
c
⃗
×
b
⃗
)
−
b
⃗
−
c
⃗
)
\vec{a} \cdot ((\vec{c} \times \vec{b}) - \vec{b} - \vec{c})
a
⋅
((
c
×
b
)
−
b
−
c
)
is equal to : 1. 32 2. 24 3. 20 4. 36
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