Let 
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
4
2 ,
3
2
7   and  
2
4
a
i
j
k b
i
j
k
c
i
j
k
= +
+
=
−
+
=
−
+
r
r
r Find a vector d
r
which is perpendicular to both 
a and 
rb
r
, and 
15
c d
⋅
rr= 13 The scalar product of the vector 
ˆ
ˆ
ˆ
i
j
k
+
+
 with a unit vector along the sum of
vectors 
ˆ
ˆ
ˆ
2
4
5
i
j
k
+
−
 and 
ˆ
ˆ
2ˆ
3
i
j
k
λ +
+
 is equal to one