The equation of the plane through the points (2 ,1 ,0 ) , (3 ,2 ,-2 ) and (3 ,1 ,7 ) is

Question

Accepted Answer

Correct answer: C. (c) : Let (x_1 ,y_1 ,z_1 ) ≡ (2 ,1 ,0 ), (x_2 ,y_2 ,z_2 ) ≡ (3 ,2 ,-2 ) , (x_3 ,y_3 ,z_3 ) ≡ (3 ,1 ,7 ) The equation of the plane passing through three points (x_1 ,y_1 ,z_1 ) , (x_2 ,y_2 ,z_2 ) and (x_3 ,y_3 ,z_3 ) is given by (x-x_1y-y_1z-z_1x_2-x_1y_2-y_1z_2-z_1x_3-x_1y_3-y_1z_3-z_1)=0 ∴(x-2y-1z-03-22-1-2-03-21-17-0)=0 ⇒(x-2y-1z11-2107)=0 ⇒ (x-2 ) (7-0 )- (y-1 ) (7+2 )+z (0-1 )=0 ⇒ 7x-14-9y+9-z=0 ⇒7x-9y-z=5

$The equation of the plane through the points (2, 1, 0), (3, 2, - 2) and (3, 1, 7) is$

Solution

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