If `vec(a) = 2 hat(i) + 2 hat(j) + hat(k) , vec(b) = - hat(i) + hat(j) + 2 hat(k)` and `vec ( c) = 3 hat(i) + hat(j)` such that `vec(a) + lambda hat`(b) is perpendicular to` vec( c)` , find `lambda`.

Explanation

`vec(a) + lambda vec(b) = ( 2 hat (i) + 2 hat (j) + hat (k)) + lambda(- hat(i) + hat(j) + 2 hat (k))`
`= ( 2 - lambda) hat(i) + ( 2 + lambda) hat(j) + ( 1 + 2 lambda) hat(k)`
`(vec(a) + lambda vec(b)) . vec(c ) = 0`
`3( 2- lambda) + ( 2 + lambda) = 0`
` 6 - 3 lambda + 2 + lambda = 0 rArr lambda = 4`