find the unit vector perpendicular to both the vectors given below p vector equal to 3 ICAP _ j cap + 4 k cap and q vector equal to
6 I cap + j cap - 8 k cap
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Answer:
a
=
i
^
−
j
^
+
k
^
b
=
i
^
+
j
^
+
k
^
Let
n
^
be a unit vector perpendicular to both
a
and
b
.
Thus,
n
^
=
∣
∣
∣
∣
a
×
b
∣
∣
∣
∣
a
×
b
∣
∣
∣
∣
a
×
b
∣
∣
∣
∣
=(
i
^
−
j
^
+
k
^
)×(
i
^
+
j
^
+
k
^
)=
k
^
−
j
^
+
k
^
−
i
^
+
j
^
−
i
^
=2(−
i
^
+
k
^
)
⇒
n
^
=
2
2
2(−
i
^
+
k
^
)
=
2
(−
i
^
+
k
^
)
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