Q11 of 181 Page 1205

Find the equation of the plane through the line of intersection of the planes and and perpendicular to the plane

Equation of plane through the line of intersection of two planes in vector form is

(1)


Where the standard equation of planes are



Putting values in equation (1), we have



(2)


Given a plane perpendicular to this plane, So if n1 and n2 are normal


vectors of planes



(


2.(2 + λ) + (-1).(-3-λ) + 1.4=0


4 + 2λ + 3 + λ + 4=0


11 + 3λ=0



Putting the value of λ in equation (2)






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Find the vector equation of the plane through the point (1, 1, 1), and passing through the intersection of the planes and

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(ii) and


(iii) and


(iv) and