Find the coordinates of the mirror image of the point P(1, 0, 0) in the line (x - 1)/2 = (y + 1)/(-3) = (z + 10)/8.

(3, -4, -2)
(5, -8, -4)
(1, -1, -10)
(2, -3, 8)

Correct answer: (5, -8, -4)

Solution

A general point on the line is Q = (1+2t, -1-3t, -10+8t). Vector PQ = (2t, -1-3t, -10+8t). For foot of perpendicular, PQ must be perpendicular to direction d=(2,-3,8): PQ.d = 4t+3+9t-80+64t = 77t-77 = 0 -> t=1. Foot F=(3,-4,-2). Reflection R = 2F - P = (2*3-1, 2*(-4)-0, 2*(-2)-0) = (5,-8,-4).

Related JEE Advanced Maths questions

Perpendiculars are drawn from points on the line (x+2)/(2) = (y+1)/(-1) = (z)/(3) to the plane x + y + z = 3. The feet of perpendiculars lie on the line -
A line ℓ passing through the origin is perpendicular to the lines ℓ₁: (3 + t) i + (-1 + 2t) j + (4 + 2t) k, -∞ < t < ∞ ℓ₂: (3 + 2s) i + (3 + 2s) j + (2 + s) k, -∞ < s < ∞ Then the coordinates(s) of the point(s) on ℓ₂ at a distance of √17 from the point of intersection of ℓ and ℓ₁ is(are)
In three-dimensional space, consider the planes P1: y = 0 and P2: x + z = 1. Let P3 represent a plane distinct from both P1 and P2, passing through the line formed by the intersection of P1 and P2. If the point (0, 1, 0) lies at a distance of 1 unit from P3, and the point (α, β, γ) lies at a distance of 2 units from P3, which of the following equations is/are valid?
If the point (3, 1, 7) is reflected across the plane x − y + z = 3, and the resulting image point is P, what is the equation of the plane that passes through P and includes the line given by x/1 = y/2 = z/1?
What is the equation of a plane that passes through the point (1, 1, 1) and is orthogonal to the planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7?
Consider a cube Q defined by the vertices {(x1, x2, x3) ∈ R³: x1, x2, x3 ∈ {0, 1}}. Let F represent the collection of all twelve lines formed by the diagonals of the six faces of the cube. Additionally, let S denote the group of four lines that pass through the main diagonals of the cube, such as the line connecting (0,0,0) and (1,1,1). If d(ℓ1, ℓ2) represents the shortest distance between two lines ℓ1 and ℓ2, determine the maximum value of d(ℓ1, ℓ2) when ℓ1 is chosen from F and ℓ2 is chosen from S.

⚔️ Practice JEE Advanced Maths free + battle 1v1 →