if unit vector a=a1i +a2j+a3k. the possible values of a1 a2 a3 are
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Answer:
We have,
∣
∣
∣
∣
∣
∣
∣
∣
a
1
b
1
c
1
a
2
b
2
c
2
a
3
b
3
c
3
∣
∣
∣
∣
∣
∣
∣
∣
2
=[abc]
2
=[(a×b).c]
2
=[∣a∣∣b∣sin
6
π
c.c]
2
=∣a∣
2
∣b∣
2
sin
2
6
π
.1(∵∣c∣=1)
=(a
1
2
+a
2
2
+a
3
2
)(b
1
2
+b
2
2
+b
3
2
)×
4
1
=
4
1
(a
1
2
+a
2
2
+a
3
2
)(b
1
2
+b
2
2
+b
3
2
)
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