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Mathematics
Mathematics
Problem
Given three vectors
a
=
6
i
^
−
3
j
^
\mathbf{a} = 6\hat{i} - 3\hat{j}
a
=
6
i
^
−
3
j
^
,
b
=
2
i
^
−
6
j
^
\mathbf{b} = 2\hat{i} - 6\hat{j}
b
=
2
i
^
−
6
j
^
and
c
=
−
2
i
^
+
21
j
^
\mathbf{c} = -2\hat{i} + 21\hat{j}
c
=
−
2
i
^
+
21
j
^
such that
α
=
a
+
b
+
c
\alpha = \mathbf{a} + \mathbf{b} + \mathbf{c}
α
=
a
+
b
+
c
. Then, the resolution of the vector
α
\alpha
α
into components with respect to
a
\mathbf{a}
a
and
b
\mathbf{b}
b
is given by a.
3
a
−
2
b
3\mathbf{a} - 2\mathbf{b}
3
a
−
2
b
b.
3
b
−
2
a
3\mathbf{b} - 2\mathbf{a}
3
b
−
2
a
c.
2
a
−
3
b
2\mathbf{a} - 3\mathbf{b}
2
a
−
3
b
d.
a
−
2
b
\mathbf{a} - 2\mathbf{b}
a
−
2
b
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