The vector equation of the plane passing through the origin and the line of intersection of the planes `vecr.veca=lamdaandvecr.vecb=mu` is

Options

A. `vecr.(lamdaveca-muvecb)=0`
B. `vecr.(lamdavecb-muveca)=0`
C. `vecr.(lamdaveca+muvecb)=0`
D. `vecr.(lamdavecb+muveca)=0`

Answer

b

Explanation

The equation of a plane through the line of intersection of the planes `vecr*veca=lamda and vecr*vecb= mu` is
`" "(vecr*veca-lamda)+k(vecr*vecb-mu)=0`
or `" "vecr*(veca+kvecb)= lamda+kmu" "`(i)
This passes through the origin, therefore
`" "vec0(veca+k vecb) = lamda+ muk or k= (-lamda)/(mu)`
Putting the value of k in (i), we get the equation of the required plane as
`" "vecr*(muveca-lamdavecb)= 0 or vecr*(lamda vecb-mu veca)=0`