#parallel lines

Sets, Relations and Functions

Let I be a set of all lines in a XY plane and R be a relation in I defined as R = (I₁, I₂):I₁ is parallel to I₂. What is

The trick is using formula we get Equivalence relation. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get Equivalence relation.

Ref: NCERT Mathematics Class XI — Sets, Relations and Functions

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Vectors and 3D Geometry

Find distance between the lines L₁ and L₂ whose vector equations are r = ; i + j + k + ; ( 3 i - j );and; r = 4 i- k + (

We know that using formula we get 2. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 2.

Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry

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Matrices and Determinants 2

The equations 2x - ky + 7 = 0 and 6x - 12y + 15 = 0 have no solution for

Recall the rule using formula we get k = 4. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get k = 4.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Linear Programming 1

In case of solution of a two variable linear programming problem by graphical method one constraint line come parallel t

We can see that we verify Infinite number of optimal solutions by full calculation: use standard identity, substitute, simplify step by step to reach Infinite number of optimal solutions.

Ref: NCERT Mathematics Class XII — Linear Programming

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