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# the unit vector perpendicular to A=2i+3j+k and B=I+j+k is

Let    and
unit vector perpendicular to  and  is detromined by taking cross product of   and  and
normalizing the cross product by dividing its magnitude in order to make unit vector .

Hence unit vector  perpendicular to  and  is ,    = (1/√6) ( 2  -  -  )
-------------------------------------------

If   , then
Above vector relation is shown in fig.1. Since  is sum of  and  , We can form a parallelogram with sides   and  .
is diagonal of parallelogram.  Since all vectors have equal magnitude , this parallelogram becomes rhombus
and is made of two equilateral triangle.

Hence each angle in the rhombus is 60o as shown in figure.  Angle between  and  is 120o .
In similar manner, we get angle between  and  is 60 if    , or
Hence ratio between angles , θ1 : θ2 = 120 : 60 = 2 : 1

Answered by Expert 25th July 2021, 4:51 PM
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