Class 12 Math: Three Dimensional Geometry Important Exam Questions
Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 12 Three Dimensional Geometry to help you test your mastery.
Exam-Pattern Questions and Answers
Question 1 (MEDIUM)
This is a descriptive problem. Work out all steps on paper before checking the solution.
Solution Explanation & Steps: a⃗+bሬ⃗+c⃗ =0ሬ⃗ (a⃗+ bሬ⃗)2= (-c⃗)2 , ⇒ a⃗+bሬ⃗.a⃗+bሬ⃗ =c⃗.c ⃗,|a⃗|2+ หbሬ⃗ห 2 + 2൫a⃗.b ሬ⃗൯= |c⃗|2 ⇒ 2 a⃗.b ሬ⃗=15, ⇒ 2 |a⃗| หbሬ⃗หcosθ=15, θ=60°
Question 2 (EASY)
- Option 1: Systematic application of coordinate rules
- Option 2: Advanced integral equations
- Option 3: Infinite boundary coordinates
- Option 4: None of the above
Solution Explanation & Steps: Studying Direction cosines and direction ratios of a line requires mastering basic coordinate relationships first.
Question 3 (MEDIUM)
- Option 1: The dependent variable
- Option 2: The constant offset
- Option 3: The complex exponent
- Option 4: The vertical coordinate
Solution Explanation & Steps: To solve algebraic equations under Direction cosines and direction ratios of a line, we isolate the single dependent variable.
Grading Step-Marking Guidelines
Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.