Consider the planes 3 x − 6 y − 2 z = 15 and 2 x + y − 2 z = 5 . Statement I The parametric equations of the line of intersection of the given planes are x = 3 + 14 t , y = 1 + 2 t and z = 15 t . Stat

Question

Consider the planes 3 x − 6 y − 2 z = 15 and 2 x + y − 2 z = 5 . Statement I The parametric equations of the line of intersection of the given planes are x = 3 + 14 t , y = 1 + 2 t and z = 15 t . Statement II The vectors 14 i ^ + 2 j ^ ​ + 15 k ^ is parallel to the line of intersection of the given planes.

TestHub · Accepted Answer

Given planes are 3 x − 6 y − 2 z = 15 and 2 x + y − 2 z = 5 For z = 0 , we get x = 3 , y = − 1 Direction ratios of planes are < 3 − 6 − 2 > and < 2 1 − 2 > then the dr's of line of intersection of planes is ⟨ 14215 ⟩ and line is 14 x − 3 ⇒ x = 2 y + 1 = 15 z − 0 = λ (say) = 14 λ + 3 , y = 2 λ − 1 , z = 15 λ Hence, Statement I is false. But Statement II is true.

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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