NCERT Class 12 · Ch 11 Exercise 11.1 · Q4
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.1 Question 4
Show that A(2,3,4),B(−1,−2,1),C(5,8,7) are collinear.
💡 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: The three points are collinear, with A the midpoint of BC.
- AB=B−A=(−3,−5,−3); AC=C−A=(3,5,3).
- AB=−AC, so the two displacements have the same line direction.
- Both lines pass through A, hence the three points are collinear. Also (B+C)/2=A.
Master Chapter 11: Three Dimensional Geometry
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Three Dimensional Geometry.
← Previous Question
Find direction cosines for a line with direction ratios (−18,12,−4).
Next Question →Find direction cosines of the sides of triangle…
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.