NCERT Class 12 · Ch 11 Exercise 11.2 · Q1
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.2 Question 1
Show that directions (12,−3,−4)/13, (4,12,3)/13 and (3,−4,12)/13 are mutually orthogonal.
💡 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: All three pairs have zero dot product.
- Each numerator has squared norm 169, so each stated direction is a unit vector.
- The three dot-product numerators are 48−36−12=0, 36+12−48=0, and 12−48+36=0.
- Dividing by 169 preserves zero. Thus each pair makes an angle π/2.
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