Q. 125.0( 1 Vote )

Show that the equ

Answer :

Given – The equation of the plane is given by ax + by + d = 0


To prove – The plane is parallel to z - axis


Tip – If ax + by + cz + d is the equation of the plane then its angle with the z - axis will be given by


Considering the equation, the direction ratios of its normal is given by (a, b, 0)


The angle the plane makes with the z - axis = sin - 1[0/√(a2 + b2)] = 0


Hence, the plane is parallel to the z - axis


To find – Equation of the plane parallel to z - axis and passing through points A = (2, - 3, 1) and B = (- 4, 7, 6)


The given equation ax + by + d = 0 passes through (2, - 3, 1) & (- 4, 7, 6)


………(i)


……(ii)


Solving (i) and (ii),


[α → arbitrary constant]




Substituting the values of a and b in eqn (i), we get,


- 2Х10α + 3Х6α + d = 0 i.e. d = - 2α


Putting the value of a, b and d in the equation ax + by + d = 0,


(- 10α)x + (- 6α)y + (- 2α) = 0


i.e. 5x + 3y + 1 = 0

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