A) \[2x-y=0\]and \[y+3z=0\]
B) \[2x-y=0\]and \[y-3z=0\]
C) \[2x+3z=0\]and \[y=0\]
D) none of the above
Correct Answer: B
Solution :
We know that the equation of a plane through the intersection of the planes \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z+{{d}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z+{{d}_{2}}=0\] is \[({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z+{{d}_{1}})+\lambda ({{a}_{2}}x+{{b}_{2}}y\]\[+{{c}_{2}}z+{{d}_{2}})=0\] where, \[\lambda \]is constant. Thus, the equation of plane \[2x\lambda -(1+\lambda )y+3z=0\] can be written as \[(2x-y)\lambda +(-y+3z)=0\] So, it is clear that the equation of plane passes through the intersection of planes \[2x-y=0\] and \[y-3z=0.\]
You need to login to perform this action.
You will be redirected in
3 sec
