VectorHard
Question
Let 
and a unit vector 
be coplanar is perpendicular to 
, then 
is equal to
and a unit vector be coplanar is perpendicular to , then is equal toOptions
A.
B.
C.
D.
Solution
It is given that is coplanar with 
and 
, we take
..... (i)
where p, q are scalars.
Since,
⏊ 
⇒ . = 0
Taking dpt product of in Eq. (i), we
⇒
⇒ 0 = p.6 + q.3 ⇒ q = - 2 p
On putting in Eq. (i), we get
⇒
⇒
⇒
⇒
⇒
⇒
⇒
= p2. 18 ⇒ 1 = p2. 18 (∵
= 1)
⇒
⇒
∴
is coplanar with and , we take ..... (i)where p, q are scalars.
Since,
⏊ ⇒
. = 0 Taking dpt product of
in Eq. (i), we⇒
⇒ 0 = p.6 + q.3 ⇒ q = - 2 p
On putting in Eq. (i), we get
⇒
⇒
⇒
⇒
⇒
⇒
⇒
= p2. 18 ⇒ 1 = p2. 18 (∵ = 1)⇒
⇒
∴
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