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Mathematics
Problem
The position vectors of four points
P
,
Q
,
R
P, Q, R
P
,
Q
,
R
and
S
S
S
are
2
a
+
4
c
,
5
a
+
3
b
+
4
c
,
−
2
b
+
c
2 \boldsymbol{a} + 4 \boldsymbol{c}, 5 \boldsymbol{a} + 3 \boldsymbol{b} + 4 \boldsymbol{c}, -2 \boldsymbol{b} + \boldsymbol{c}
2
a
+
4
c
,
5
a
+
3
b
+
4
c
,
−
2
b
+
c
and
2
a
+
c
2 \boldsymbol{a} + \boldsymbol{c}
2
a
+
c
respectively. Prove that
P
Q
PQ
P
Q
is parallel to
R
S
RS
R
S
.
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