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Mathematics
Mathematics
Problem
The vector
a
=
α
i
^
+
2
j
^
+
β
k
^
\mathbf{a} = \alpha\hat{i} + 2\hat{j} + \beta\hat{k}
a
=
α
i
^
+
2
j
^
+
β
k
^
lies in the plane of the vectors
b
=
i
^
+
j
^
\mathbf{b} = \hat{i} + \hat{j}
b
=
i
^
+
j
^
and
c
=
j
^
+
k
^
\mathbf{c} = \hat{j} + \hat{k}
c
=
j
^
+
k
^
and bisects the angle between
b
\mathbf{b}
b
and
c
\mathbf{c}
c
. Then, which one of the following gives possible values of
α
\alpha
α
and
β
\beta
β
? a.
α
=
1
,
β
=
1
\alpha = 1, \beta = 1
α
=
1
,
β
=
1
b.
α
=
2
,
β
=
2
\alpha = 2, \beta = 2
α
=
2
,
β
=
2
c.
α
=
1
,
β
=
2
\alpha = 1, \beta = 2
α
=
1
,
β
=
2
d.
α
=
2
,
β
=
1
\alpha = 2, \beta = 1
α
=
2
,
β
=
1
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