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Mathematics
Mathematics
Problem
If
a
=
−
i
^
+
j
^
+
k
^
\mathbf{a} = -\hat{i} + \hat{j} + \hat{k}
a
=
−
i
^
+
j
^
+
k
^
and
b
=
2
i
^
+
k
^
\mathbf{b} = 2\hat{i} + \hat{k}
b
=
2
i
^
+
k
^
, then find the vector
x
\mathbf{x}
x
satisfying the conditions. (i) that it is coplanar with
a
\mathbf{a}
a
and
b
\mathbf{b}
b
. (ii) it is perpendicular to
b
\mathbf{b}
b
. (iii)
a
⋅
x
=
7
\mathbf{a} \cdot \mathbf{x} = 7
a
⋅
x
=
7
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