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Mathematics
Mathematics
Problem
If
i
^
−
3
j
^
+
k
^
\hat{i} - 3\hat{j} + \hat{k}
i
^
−
3
j
^
+
k
^
bisects the angle between
a
\mathbf{a}
a
and
−
i
^
+
2
j
^
+
2
k
^
-\hat{i} + 2\hat{j} + 2\hat{k}
−
i
^
+
2
j
^
+
2
k
^
, where
a
\mathbf{a}
a
is a unit vector, then a.
a
=
1
105
(
41
i
^
+
88
j
^
−
40
k
^
)
\mathbf{a} = \frac{1}{105}(41\hat{i} + 88\hat{j} - 40\hat{k})
a
=
105
1
(
41
i
^
+
88
j
^
−
40
k
^
)
b.
a
=
1
105
(
41
i
^
+
88
j
^
+
40
k
^
)
\mathbf{a} = \frac{1}{105}(41\hat{i} + 88\hat{j} + 40\hat{k})
a
=
105
1
(
41
i
^
+
88
j
^
+
40
k
^
)
c.
a
=
1
105
(
−
41
i
^
+
88
j
^
−
40
k
^
)
\mathbf{a} = \frac{1}{105}(-41\hat{i} + 88\hat{j} - 40\hat{k})
a
=
105
1
(
−
41
i
^
+
88
j
^
−
40
k
^
)
d.
a
=
1
105
(
41
i
^
−
88
j
^
−
40
k
^
)
\mathbf{a} = \frac{1}{105}(41\hat{i} - 88\hat{j} - 40\hat{k})
a
=
105
1
(
41
i
^
−
88
j
^
−
40
k
^
)
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