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Mathematics
Mathematics
Problem
The vectors
p
=
2
i
^
−
j
^
+
k
^
\mathbf{p}=2\hat{i}-\hat{j}+\hat{k}
p
=
2
i
^
−
j
^
+
k
^
and
q
=
3
i
^
+
4
j
^
+
λ
k
^
\mathbf{q}=3\hat{i}+4\hat{j}+\lambda\hat{k}
q
=
3
i
^
+
4
j
^
+
λ
k
^
form two sides of a triangle. If the area of the triangle is
5
2
5\sqrt{2}
5
2
square units, determine the value(s) of
λ
\lambda
λ
.
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