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Mathematics
Problem
The plane passing through the origin contains the vectors
u
=
2
i
+
k
\mathbf{u}=2\mathbf{i}+\mathbf{k}
u
=
2
i
+
k
and
v
=
i
−
3
j
\mathbf{v}=\mathbf{i}-3\mathbf{j}
v
=
i
−
3
j
. Which of the following is a unit vector normal to this plane whose
y
y
y
-component is negative? a)
1
46
(
3
i
+
j
−
6
k
)
\dfrac{1}{\sqrt{46}}\,( 3\mathbf{i}+\mathbf{j}-6\mathbf{k} )
46
1
(
3
i
+
j
−
6
k
)
b)
1
46
(
−
3
i
−
j
+
6
k
)
\dfrac{1}{\sqrt{46}}\,( -3\mathbf{i}-\mathbf{j}+6\mathbf{k} )
46
1
(
−
3
i
−
j
+
6
k
)
c)
1
46
(
−
3
i
−
j
+
6
k
)
\dfrac{1}{46}\,( -3\mathbf{i}-\mathbf{j}+6\mathbf{k} )
46
1
(
−
3
i
−
j
+
6
k
)
d)
1
10
(
−
3
i
−
j
+
6
k
)
\dfrac{1}{\sqrt{10}}\,( -3\mathbf{i}-\mathbf{j}+6\mathbf{k} )
10
1
(
−
3
i
−
j
+
6
k
)
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