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Mathematics
Mathematics
Problem
Vectors
a
⃗
=
3
i
^
+
2
j
^
+
k
^
\vec a = 3\hat i + 2\hat j + \hat k
a
=
3
i
^
+
2
j
^
+
k
^
and
b
⃗
=
−
i
^
+
4
j
^
+
2
k
^
\vec b = -\hat i + 4\hat j + 2\hat k
b
=
−
i
^
+
4
j
^
+
2
k
^
represent the two adjacent sides of a triangle when placed tail-to-tail. (i) Write an expression for the area of the triangle in terms of
a
⃗
\vec a
a
and
b
⃗
\vec b
b
. (ii) Calculate the numerical value of this area.
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