Class 12 Three Dimensional Geometry · Long Answer3 Marksprojection_and_reflection
Class 12 Maths · Three Dimensional Geometry · Long Answer #41
Find the foot and distance from P=(0,2,3) to r=(-3,1,-4)+t(5,2,3), t∈ℝ.
✅ Step-by-Step Solution
Final Answer: Foot H=(2,3,-1); distance=sqrt(21).
- Write H=A+td and impose (P−H)·d=0.
- A=(-3,1,-4), d=(5,2,3), P−A=(3,1,7); t=((P−A)·d)/(d·d)=1.
- H=A+td=(2,3,-1). Check (P−H)·d=0.
- |P−H|=√(21)=sqrt(21). Foot H=(2,3,-1); distance=sqrt(21).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write H=A+td and impose (P−H)·d=0.
- [1 mark] A=(-3,1,-4), d=(5,2,3), P−A=(3,1,7); t=((P−A)·d)/(d·d)=1.
- [1 mark] H=A+td=(2,3,-1). Check (P−H)·d=0.
- [0.5 marks] |P−H|=√(21)=sqrt(21). Foot H=(2,3,-1); distance=sqrt(21).
Master Chapter 11: Three Dimensional Geometry
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Three Dimensional Geometry.
← Previous Question
Find vector and Cartesian equations of the line through (2,-1,4)…
Next Question →Find the vector equation through (1,2,−1) parallel to 5x−25=14−7y=35z.
More Practice Questions in Three Dimensional Geometry
Related Questions in Three Dimensional Geometry
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the foot of the perpendicular from (2,−3,4) to the y-axis.
Class 12 Three Dimensional Geometry · Mcq Single Correct
A line makes angles α,β,γ with the positive coordinate axes. Find cos 2α+cos 2β+cos 2γ.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the distance of (α,β,γ) from the y-axis.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find direction cosines of (x−1)/2=(1−y)/3=(2z−1)/12.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the acute angle between two distinct body diagonals of a cube.
Class 12 Three Dimensional Geometry · Mcq Single Correct
A line makes angles θ₁,θ₂,θ₃,θ₄ with the four body diagonals of a cube. Find Σ cos²θᵢ.