JEE Main202622 January 2026Morning ShiftMathematicsThree Dimensional GeometryActual

If the image of the point P (1,2, a) in the line x-6 3 = y-7 2 = 7- z 2 is Q (5, b, c ) , then a²+b²+c² is equal to

Options

A298
B293
C264
D283

Correct answer

A. 298

Step-by-step solution

Line: point (6,7,7) , direction (3,2,-2) . General point on line: (6+3t, 7+2t, 7-2t) . Foot of perpendicular from P(1,2,a) : PM (3,2,-2) = 0 . 3(5+3t)+2(5+2t)-2(7-2t-a) = 0 17t+11+2a = 0 . Image Q = 2M - P = (11+6t, 12+4t, 14-4t-a) . Given Q_x = 5 : 11+6t = 5 t = -1 . From 17(-1)+11+2a = 0 a = 3 . b = 12+4(-1) = 8 , c = 14-4(-1)-3 = 15 . a^2+b^2+c^2 = 9+64+225 = 298 .

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

Let P be the plane such that it contains the straight line x-1 2 = y-3 3 = z+2 1 and is perpendicular to the plane x + 2y + 3z = 4 . Let P₁ be the plane which passes through the po 2026 Let L be the straight line joining the points P(1, 2, -1) and Q(2, 3, 1) . Let S be the foot of the perpendicular drawn from the point R(4, -1, 5) to the line L . Another line pass 2026 Let the foot of perpendicular from the point ( , 2, 3) on the line x-4 1 = y-9 2 = z-5 1 be the point (1, , 2) . Then the distance between the lines x-1 2 = y-2 3 = z+4 6 and x- 2 2026 Let a line L₁ pass through the origin and be perpendicular to the lines L₂: r = (3+t) i + (2t-1) j + (2t+4) k and L₃: r = (3+2s) i + (3+2s) j + (2+s) k , t, s R . If (a, b, c) , a 2026 The shortest distance between the lines x-4 1 = y-3 2 = z-2 -3 and x+2 2 = y-6 4 = z-5 -5 is : 2026 Let the image of the point P(0, -5, 0) in the line x-1 2 = y 1 = z+1 -2 be the point R and the image of the point Q (0, -1 2 , 0 ) in the line x-1 -1 = y+9 4 = z+1 1 be the point S 2026 Let the image of the point P(1, 6, a) in the line L: x 1 = y-1 2 = z-a+1 b , b > 0 , be ( a 3 , 0, a+c ) . If S( , , ) , > 0 , is the point on L such that the distance of S from th 2026 Let a line L be perpendicular to both the lines L₁: x+1 3 = y+3 5 = z+5 7 and L₂: x-2 1 = y-4 4 = z-6 7 . If is the acute angle between the lines L and L₃: x - 8 7 2 = y - 4 7 1 = 2026 Full Three Dimensional Geometry list All JEE Main PYQs