67. Find a unit vector parallel to the xy plane and perpendicular to the vector 4i - 3j+k.
68, show that A = (21 - 2j+k)/3, B = (1 + 24 + 2k)/3 and C = (21 +3 -- 2k)/3 are mutually orthogonal unit vectors
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The vector parallel to xy plane is perpendicular to
k
^
in the z-direction
∴
k
^
×(4
i
^
−3
j
^
+
k
^
)=(4
j
^
+3
i
^
) is the vector in the x−y plane perpendicular to both
k
^
and the given vector
∴ the required unit vector
=
∣
∣
∣
∣
3
i
^
+4
j
^
∣
∣
∣
∣
3
i
^
+4
j
^
=
3
2
+4
2
3
i
^
+4
j
^
=±
5
1
(3
i
^
+4
j
^
)
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