If three vectors along coordinate axes represent the adjacent sides of a cube of side b, then the unit vector
along its diagonal passing through the origin is
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Point diagonal line(0,0,0) and (b,b,b)
Vector along diagonal,
B
=(b−o)
i
^
+(b−o)
j
^
+(b−o)
k
^
=b
i
^
+b
j
^
+b
k
^
Unit vector along diagonal,
B
^
=
∣
∣
∣
∣
B
∣
∣
∣
∣
B
=
b
2
+b
2
+b
2
b
i
^
+b
j
^
+b
k
^
=
3
i
^
+
j
^
+
k
^
Hence, unit vector along diagonal is
3
i
^
+
j
^
+
k
^
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