If A = 2i + j and B = i - j + 5k . Find unit vector perpendicular to A x B .
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Answer:
We know that cross product of any two vectors yields a vector which is perpendicular to both vectors
∴ for two vectors
A
and
B
if
C
is the vector perpendicular to both.
C
=
A
×
B
=
⎣
⎢
⎢
⎡
i
A
1
B
1
j
A
2
B
2
k
A
3
B
2
⎦
⎥
⎥
⎤
=(A
2
b
3
−B
2
a
3
)
i
−(A
1
B
3
−B
1
A
3
)
j
+(A
1
B
2
−b
1
A
2
)
k
inserting given vectors we obtain
C
=
⎣
⎢
⎢
⎡
i
2
1
j
1
−1
k
1
2
⎦
⎥
⎥
⎤
=(1×2−(−1)×1)
i
−(2×2−1×1)
j
+(2×(−1)−1×1)
k
=3
i
−3
j
−3
k
Now unit vector in the direction of
C
is
∣
C
∣
C
∴∣
C
∣=
3
3
+(−3)
2
+(−3)
2
=
27
=3
3
Therefore desired unit vector is
3
1
(
i
−
j
−
k
)
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