NCERT Class 12 · Ch 11 Exercise 11.2 · Q6
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.2 Question 6
Find the Cartesian equation through (−2,4,−5) parallel to (x+3)/3=(y−4)/5=(z+8)/6.
💡 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: r=(-2,4,-5)+t(3,5,6), t∈ℝ; Cartesian: (x−(-2))/(3)=(y−(4))/(5)=(z−(-5))/(6).
- A line through base A in nonzero direction d has r=A+td.
- Here A=(-2,4,-5), d=(3,5,6).
- Equating components gives r=(-2,4,-5)+t(3,5,6), t∈ℝ. Eliminating t gives (x−(-2))/(3)=(y−(4))/(5)=(z−(-5))/(6).
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 through (2,−1,4) with direction…
Next Question →Write the vector form of (x−5)/3=(y+4)/7=(z−6)/2.
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.