The equation of the plane containing the lines `vecr=(hati+hatj-hatk)+lamda(3hati-hatj)` and `vecr=(4hati-hatk)+mu(2hati+3hatk)`, is

Options

A. `vecr.(3hati+9hatj-2hatk)+14=0`
B. `vecr.(3hati+9hatj+2hatk)=14`
C. `vecr.(3hati+9hatj-2hatk)=14`
D. none of these

Answer

C

Explanation

Here `veca_(1)=hati+hatj-hatk, vecb_(1)=3hati-3hatj, veca_(2)=4hati+0hatj-hatk,`
`vecb-3hati-hatj` and `vecb_(2)=2hati+0hatj+3hatk`
The equation of the plane containing the given lines is
`[(vecr,vecb_(1),vecb_(2)]=[(veca_(1),vecb_(1),vecb_(2))]`
`impliesvecr.(vecb_(1)xxvecb_(2))=11`
`impliesvecr.(-3hati-9hatj+2hatk)=-14 [:' vecb_(1)xxvecb_(2)-3hati-9hatj+2hatk]`
`impliesvecr.(3hati+9hatj-2hatk)=14`