If the origin and the points P ( 2 , 3 , 4 ) , Q ( 1 , 2 , 3 ) and R ( x , y , z ) are co-planar then

Question

If the origin and the points P ( 2 , 3 , 4 ) , Q ( 1 , 2 , 3 ) and R ( x , y , z ) are co-planar then, x - 2 y - z = 0, x + 2 y + z = 0, x - 2 y + z = 0, 2 x - 2 y + z = 0

MARKS App · Accepted Answer

O , P , Q , R are co-planar ⇒ O R ¯ O P ¯ O Q ¯ = 0 ⇒ x y z 2 3 4 1 2 3 = 0 ⇒ x 9 - 8 - y 6 - 4 + z 4 - 3 = 0 ⇒ x - 2 y + z = 0 Alternative Points P , Q satisfy equations given in option.

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