PD is the required distance to be determined, which
is the projection of AP
uuur
 on AB
AC
×
uuur
uuur © NCERT
not to be republished
 MATHEMATI CS
496
Hence, PD = the dot product of AP
uuur
  with the unit vector along AB
AC
×
uuur
uuur So
AP
uuur
= 3 
k
j
i
7ˆ
6ˆ
ˆ
+
+
and
AB
AC
×
uuur
uuur
=
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
2
3
2
12
16
12
4
0
4
i
j
k
i
j
k
=
−
+
−
Unit vector along AB
AC
×
uuur
uuur
=
ˆ
ˆ
ˆ
3
4
3
34
i
j
k
−
+
Hence
PD = (
)ˆ
7
6ˆ
3ˆ
k
j
i
+
+ ˆ
ˆ
ˆ
3
4
3
34
i
j
k
−
+
=
17
34
3
Alternatively, find the equation of the plane passing through A, B and C and then
compute the distance of the point P from the plane