VectorHard
Question
Let 
. If 
is a unit vector such that 
then equals
. If is a unit vector such that then equalsOptions
A.
B.
C.
D.
Solution
Let 
where x2 + y2 + z2 = 1 .....(i) (∵
being unit vector)
Since,
⇒ x - y = 0 ⇒ x = y .....(ii)
Alos,
⇒
⇒ x + y + z = 0
⇒ 2x + z = 0 [from Eq. (ii)] ........(iii)
From Eqs. (i), (ii) and (iii), we get
x2 + x2 + 4x2 = 1
⇒
∴
where x2 + y2 + z2 = 1 .....(i) (∵
being unit vector) Since,
⇒ x - y = 0 ⇒ x = y .....(ii)
Alos,
⇒
⇒ x + y + z = 0
⇒ 2x + z = 0 [from Eq. (ii)] ........(iii)
From Eqs. (i), (ii) and (iii), we get
x2 + x2 + 4x2 = 1
⇒
∴
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