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Mathematics
Mathematics
Problem
Let
a
=
i
^
+
j
^
\mathbf{a} = \hat{i} + \hat{j}
a
=
i
^
+
j
^
,
b
=
j
^
+
k
^
\mathbf{b} = \hat{j} + \hat{k}
b
=
j
^
+
k
^
and
c
=
α
a
+
β
b
\mathbf{c} = \alpha\mathbf{a} + \beta\mathbf{b}
c
=
α
a
+
β
b
. If the vectors,
i
^
−
2
j
^
+
k
^
\hat{i} - 2\hat{j} + \hat{k}
i
^
−
2
j
^
+
k
^
,
3
i
^
+
2
j
^
−
k
^
3\hat{i} + 2\hat{j} - \hat{k}
3
i
^
+
2
j
^
−
k
^
and
c
\mathbf{c}
c
are coplanar, then
α
β
\frac{\alpha}{\beta}
β
α
is equal to a. 1 b. 2 c. 3 d. -3
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