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Mathematics
Mathematics
Problem
The vector
v
⃗
=
3
i
−
λ
j
+
2
λ
k
\vec{v}=3\mathbf{i}-\lambda\mathbf{j}+2\lambda\mathbf{k}
v
=
3
i
−
λ
j
+
2
λ
k
is perpendicular to
a
⃗
=
i
+
5
j
+
k
\vec{a}=\mathbf{i}+5\mathbf{j}+\mathbf{k}
a
=
i
+
5
j
+
k
and parallel to
b
⃗
=
6
i
−
2
j
+
4
k
\vec{b}=6\mathbf{i}-2\mathbf{j}+4\mathbf{k}
b
=
6
i
−
2
j
+
4
k
. Determine the value of
λ
\lambda
λ
.
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