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Mathematics
Mathematics
Problem
Let
a
=
2
i
^
−
j
^
+
k
^
\mathbf{a}=2\hat{i}-\hat{j}+\hat{k}
a
=
2
i
^
−
j
^
+
k
^
and
b
=
i
^
+
3
j
^
−
2
k
^
\mathbf{b}=\hat{i}+3\hat{j}-2\hat{k}
b
=
i
^
+
3
j
^
−
2
k
^
. Define
c
=
a
+
t
b
\mathbf{c}=\mathbf{a}+t\mathbf{b}
c
=
a
+
t
b
, where
t
∈
R
t\in\mathbb{R}
t
∈
R
. Find all real values of
t
t
t
for which the area of the parallelogram having
a
\mathbf{a}
a
and
c
\mathbf{c}
c
as adjacent sides is
10
10
10
square units.
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