Determine the vector equation of the line passing through (1, 2, 3) and parallel to the planes x − y + 2z = 5 and 3x + y + z = 6. A. r = (i + 2j + 3k) + λ(−3i + 5j + 4k) B. r = (i + 2j + 3k) + λ(3i + 5j + 4k) C. r = (i + 2j + 3k) + λ(−i + j + k) D. r = (i + 2j + 3k) + λ(2i + 2j − k) Answer: A) r = (i + 2j + 3k) + λ(−3i + 5j + 4k) Explanation: Direction is cross product of normals: (1, −1, 2) and (3, 1, 1). n₁ × n₂ = i(−1−2) − j(1−6) + k(1+3) = −3i + 5j + 4k.

imo class 12 three dimensional geometry

Determine the vector equation of the line passing through (1, 2, 3) and parallel to the planes x − y + 2z = 5 and 3x + y + z = 6.

VAVidaara Admin Asked 6d ago 0 views 0 answers

Determine the vector equation of the line passing through (1, 2, 3) and parallel to the planes x − y + 2z = 5 and 3x + y + z = 6.

Answer: A) r = (i + 2j + 3k) + λ(−3i + 5j + 4k)

Explanation: Direction is cross product of normals: (1, −1, 2) and (3, 1, 1). n₁ × n₂ = i(−1−2) − j(1−6) + k(1+3) = −3i + 5j + 4k.

No comments yet — start the discussion.