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Mathematics
Problem
Given the vectors
a
=
2
i
^
−
j
^
+
3
k
^
\mathbf{a}=2\hat{i}-\hat{j}+3\hat{k}
a
=
2
i
^
−
j
^
+
3
k
^
,
b
=
−
i
^
+
4
j
^
−
2
k
^
\mathbf{b}=-\hat{i}+4\hat{j}-2\hat{k}
b
=
−
i
^
+
4
j
^
−
2
k
^
and
c
=
5
i
^
+
2
j
^
+
4
k
^
\mathbf{c}=5\hat{i}+2\hat{j}+4\hat{k}
c
=
5
i
^
+
2
j
^
+
4
k
^
, find the vector
r
=
2
a
−
b
+
c
\mathbf{r}=2\mathbf{a}-\mathbf{b}+\mathbf{c}
r
=
2
a
−
b
+
c
in unit-vector form. Also calculate
∣
r
∣
|\mathbf{r}|
∣
r
∣
.
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