For the vector `vecA=a hati+2hatj-hatj and vecB =2ahati-ahatj+4hatk` to the perpendicular to each other , find the value of a.

Explanation

Two vectors are perpendicular if their scalar product is zero
`vecA.vecB=0`
`rArr (ahati+2hatj-hatk).(2ahati-ahatj+4hatk)=0`
`rArr axx2a-2xxa-1xx4=0`
`rArr2a^(2)-2a-4=0`
`rArr a^(2)-a-2=0`
`a^(2)-2a+a-2=0`
`a(a-2)+1(a-2)=0`
`(a+1)(a-2)=0`
`a=-1 or 2`