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Mathematics
Mathematics
Problem
If
a
=
i
^
+
j
^
+
k
^
\mathbf{a} = \hat{i} + \hat{j} + \hat{k}
a
=
i
^
+
j
^
+
k
^
,
b
=
4
i
^
+
5
j
^
+
4
k
^
\mathbf{b} = 4\hat{i} + 5\hat{j} + 4\hat{k}
b
=
4
i
^
+
5
j
^
+
4
k
^
and
c
=
i
^
+
α
j
^
+
β
k
^
\mathbf{c} = \hat{i} + \alpha\hat{j} + \beta\hat{k}
c
=
i
^
+
α
j
^
+
β
k
^
are linearly dependent vectors and
∣
c
∣
=
3
|\mathbf{c}| = \sqrt{3}
∣
c
∣
=
3
, then a.
α
=
1
,
β
=
−
1
\alpha = 1, \beta = -1
α
=
1
,
β
=
−
1
b.
α
=
1
,
β
=
±
1
\alpha = 1, \beta = \pm 1
α
=
1
,
β
=
±
1
c.
α
=
−
1
,
β
=
±
1
\alpha = -1, \beta = \pm 1
α
=
−
1
,
β
=
±
1
d.
α
=
±
1
,
β
=
1
\alpha = \pm 1, \beta = 1
α
=
±
1
,
β
=
1
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