Class 12 Three Dimensional Geometry · Very Long Answer5 Marksdistance_to_origin
Class 12 Maths · Three Dimensional Geometry · Very Long Answer #58
R=(4,y,z) lies on the segment joining P(2,−3,4),Q(8,0,10). Find its distance from the origin.
✅ Step-by-Step Solution
Final Answer: 2√14.
- Q−P=(6,3,6); write R=P+t(Q−P).
- Its x-coordinate gives 2+6t=4, so t=1/3∈[0,1].
- Then y=−3+3/3=−2 and z=4+6/3=6.
- |R|²=4²+(−2)²+6²=56.
- The distance is √56=2√14.
📋 CBSE Stepwise Marking Scheme
- [1 mark] Q−P=(6,3,6); write R=P+t(Q−P).
- [1 mark] Its x-coordinate gives 2+6t=4, so t=1/3∈[0,1].
- [1 mark] Then y=−3+3/3=−2 and z=4+6/3=6.
- [1 mark] |R|²=4²+(−2)²+6²=56.
- [1 mark] The distance is √56=2√14.
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