If the distance between the plane A x − 2 y + z = d and the plane containing the lines 2 x − 1 = 3 y − 2 = 4 z − 3 and 3 x − 2 = 4 y − 3 = 5 z − 4 is 6 , then ∣ d ∣ is

Question

If the distance between the plane A x − 2 y + z = d and the plane containing the lines 2 x − 1 ​ = 3 y − 2 ​ = 4 z − 3 ​ and 3 x − 2 ​ = 4 y − 3 ​ = 5 z − 4 ​ is 6 ​ , then ∣ d ∣ is

TestHub · Accepted Answer

Equation of plane containing the given lines is ​ x − 1 2 3 ​ y − 2 3 4 ​ z − 3 4 5 ​ ​ = 0 ⇒ ⇒ ⇒ ​ ( x − 1 ) ( − 1 ) − ( y − 2 ) ( − 2 ) + ( z − 3 ) ( − 1 ) = 0 − x + 1 + 2 y − 4 − z + 3 = 0 − x + 2 y − z = 0 … ( i ) ​ Given plane is x − 2 y + z = d Eqs. (i) and (ii) are parallel. Clearly, A = 1 Now, distance between plane ​ = ​ 1 + 4 + 1 ​ d ​ ​ = 6 ​ ⇒ ∣ d ∣ = 6 ​

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

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