Class 12 Three Dimensional Geometry · Very Long Answer5 Marksdistance_along_line
Class 12 Maths · Three Dimensional Geometry · Very Long Answer #54
Find the line through A(1,2,3),B(3,5,9), and its points at distance 14 from B.
✅ Step-by-Step Solution
Final Answer: r=(1,2,3)+t(2,3,6); points (7,11,21),(−1,−1,−3).
- B−A=(2,3,6)=d, with |d|=7.
- The vector line is r=A+td; Cartesian form (x−1)/2=(y−2)/3=(z−3)/6.
- Write a point relative to B as X=B+sd. Then |X−B|=7|s|=14.
- Thus s=±2; evaluate B±2d.
- The required points are (7,11,21) and (−1,−1,−3).
📋 CBSE Stepwise Marking Scheme
- [1 mark] B−A=(2,3,6)=d, with |d|=7.
- [1 mark] The vector line is r=A+td; Cartesian form (x−1)/2=(y−2)/3=(z−3)/6.
- [1 mark] Write a point relative to B as X=B+sd. Then |X−B|=7|s|=14.
- [1 mark] Thus s=±2; evaluate B±2d.
- [1 mark] The required points are (7,11,21) and (−1,−1,−3).
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