Find the equation of the plane through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane `x-2y+4z=1.` Also show that the plain thus obtained contains the line ` vec r=- hat i+3 hat j+4 hat k+lambda(3 hat i-2 hat j-5 hat k)dot`

Explanation

Let the equation of plane through (2,1,-1) be


a(x-2)+b(y-1)+c(z+1)=0 {...(i) }


because (i) passes through (-1,3,4)



therefore,` a(-1-2)+b(3-1)+c(4+1)=0 `

...