If `f(x)=2x+1` and `g(x)=x/2`, then find `(fog(x))-(gof(x))`

Answer

c

Explanation

For the given lines, let `vec(a_1) =hati+hatj-hatk, vec(a_2)= 4hati-hatk, vec(b_1) = 3hati-hatj and vec(b_2) = 2hati+3hatk`. Therefore,
`" "[vec(a_(2))-vec(a_(1))vec(b_1)vec(b_2)]=|{:(4-1,,0-1,,-1+1),(3,,-1,,0),(2,,0,,3):}|`
`" "= |{:(3,,-1,,0),(3,,-1,,0),(2,,0,,3):}|=0`
Hence, the lines are coplanar. Also vector `vec(b_1) adn vec(b_2)` along which the lines are directed are not collinear.
Hence, the lines intersect. When `vecbxxvecd=vec0` , vectors and `vecr=vecc+lamdavecd` are parallel and do not intersect. But this statement is not the correct explanation for Statement 1.