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Three Dimensional Geometry
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
Prove that lines $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4}$ and $\dfrac{x-2}{3} = \dfrac{y-3}{4} = \dfrac{z-4}{5}$ are coplanar and find point of intersection.
Step-by-Step Solution
Given: Prove that lines $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4}$ and $\dfrac{x-2}{3} = \dfrac{y-3}{4} = \dfrac{z-4}{5}$ are coplanar and find point of intersection. Step 1: Formulate initial mathematical setup / substitution: Given equation / conditions: $$Determinant$$ [1.0 Mark] Step 2: Perform intermediate algebraic / calculus operations: Executing the step-by-step reduction: $$0$$ [1.0 Mark] Step 3: Evaluate final values / boundary conditions: Substituting limits or solving the simplified system: $$> Coplanar. Intersection point (-1, -1, -1).$$ [1.0 Mark] Conclusion: The final evaluated answer is > Coplanar. Intersection point (-1, -1, -1)..
--- 🎯 Official CBSE Marking Scheme: Formulating mathematical relation: 1.0 Mark Executing algebraic/calculus operations: 1.0 Mark Evaluating final solution/vector: 1.0 Mark
Correct Answer:
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