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The vector equation of the plane passi...

The vector equation of the plane passing through the origin and the line of intersection of the planes ` vec rdot vec a=lambdaa n d vec rdot vec b=mu` is (a) ` vec rdot(lambda vec a-mu vec b)=0` (b) ` vec rdot(lambda vec b-mu vec a)=0` (c) ` vec rdot(lambda vec a+mu vec b)=0` (d) ` vec rdot(lambda vec b+mu vec a)=0`

A

`vecr.(lamdaveca-muvecb)=0`

B

`vecr.(lamdavecb-muveca)=0`

C

`vecr.(lamdaveca+muvecb)=0`

D

`vecr.(lamdavecb+muveca)=0`

Text Solution

Verified by Experts

The correct Answer is:
b
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`
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