Find the angle between the line `vecr=(hati+2hatj-hatk)+lamda(hati-hatj+hatk)` and the plane `ver.(2hati-hatj+hatk)=4`

Explanation

We know that if `theta` is the angle between the lines `vecr=veca+lamdavecb and vecr*vecn=p`, then `sintheta=|(vecb*vecn)/(|vecb||vecn|)|`
Therefore, if `theta` is the angle between `vecr=hati+2hatj-hatk+lamda(hati-hatj+hatk) and vecr*(2hati-hatj+hatk)=4,` then
`" "sin theta=|((hati-hatj+hatk)*(2hati-hatj+hatk))/(|hati-hatj+hatk||2hati-hatj+hatk|)|`
`" "=(2+1+1)/(sqrt(1+1+1)sqrt(4+1+1))`
`" "=(4)/(sqrt(3)sqrt(6))=(4)/(3sqrt2)`
or `" "theta=sin^(-1)((4)/(3sqrt2))`