If a,b,c. are unit vectors such that a+b+c=ő, find the value of
Den
and defined
a b+b. c+c. a.
Answers
Answer:
the answer is
Explanation:
Let θ
1
, be the angle between a and b,θ
2
be the angle between c and d
and ϕ be angle between a×b and c×d then
(a×b).(c×d)=1⇒∣a×b∣∣c×d∣cosϕ=1
⇒sinθ
1
sinθ
2
cosϕ=1
⇒θ
1
=π/2,θ/2=π/2,ϕ=0
As ϕ=0 so a×b and c×d. are parallel
⇒a,b,c,d are coplanar Also a⋅c=1/2⇒cosθ
3
=1/2
(where θ
3
is the angle between a and c )
θ
3
=π/2⇒ angle between a and c is π/3
⇒ angle between b and d is π/3
∴b and d are non-parallel
Let θ
1
, be the angle between a and b,θ
2
be the angle between c and d
and ϕ be angle between a×b and c×d then
(a×b).(c×d)=1⇒∣a×b∣∣c×d∣cosϕ=1
⇒sinθ
1
sinθ
2
cosϕ=1
⇒θ
1
=π/2,θ/2=π/2,ϕ=0
As ϕ=0 so a×b and c×d. are parallel
⇒a,b,c,d are coplanar Also a⋅c=1/2⇒cosθ
3
=1/2
(where θ
3
is the angle between a and c )
θ
3
=π/2⇒ angle between a and c is π/3
⇒ angle between b and d is π/3
∴b and d are non-parallel
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