Home › UP Board Class 12 › Mathematics › Three Dimensional Geometry › The vector equation of a line passing through po…
The vector equation of a line passing through point a and parallel to vector b is
Ar = a × b
Br = a · b
Cr = a + λb
Dr = λa + b
Answer & Solution
Correct answer: C. r = a + λb
1. A line through point a in the direction of b is the set of all r reachable by moving from a along b.
2. The position vector is r = a + λb, where λ is the scalar parameter.
3. Varying λ traces the entire line.
4. So option C is correct.
_Source: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.3.1_
Related questions
The image of the point (1, 2, 3) in the plane x + y + z = 0 isThe foot of the perpendicular from origin to the plane 2x + 3y - 6z = 14 isThe line through the origin with direction ratios (1, 1, 1) meets the plane x + y + z = 6 A line has direction ratios (1, 1, 2) and meets the plane x - y + z = 0. The angle ϕ betweThe plane through the points (1,1,0), (1,0,1) and (0,1,1) has equationThe equation of a plane parallel to x + 2y - 3z = 5 and passing through (1, 1, 1) isThe shortest distance between r = (1,2,3) + λ(2,3,4) and r = (2,4,5) + μ(3,4,5) isThe line r = (2, -1, 4) + λ(3, 0, 2), expressed in symmetric Cartesian form, is