NCERT Class 12 · Ch 11 Exercise 11.2 · Q7
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.2 Question 7
Write the vector form of (x−5)/3=(y+4)/7=(z−6)/2.
💡 Concept Hints
- Identify the base point and a nonzero direction before applying a vector formula.
- Use dot products for angles, proportional directions for parallelism, and a triple product for skew-line distance.
✅ Step-by-Step Solution
Final Answer: r=(5,-4,6)+t(3,7,2), t∈ℝ; Cartesian: (x−(5))/(3)=(y−(-4))/(7)=(z−(6))/(2).
- A line through base A in nonzero direction d has r=A+td.
- Here A=(5,-4,6), d=(3,7,2).
- Equating components gives r=(5,-4,6)+t(3,7,2), t∈ℝ. Eliminating t gives (x−(5))/(3)=(y−(-4))/(7)=(z−(6))/(2).
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