Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Paragraph Let f( x )= ae ^ 2 x + be ^ x + cx satisfies the condition f(0)=-1, f^ ( 2)=31 and ₀^ 4 (f( x )- cx ) dx = 39 2 . Image of a line x-1 3 = y-3 5 = z-4 2 in the plane (a-3) x+(b+a) y+z+c=0 be a line L=0 whose direction ratios are 1, p , q respectively. Let = a i + b j + c k and m =( p -2) i +2 j +( q +3) k . On the basis of above information, answer the following : Question Component of vector which is perpen

Options

  1. A20 i -12 j +12 k
  2. B5 i -6 j +3 k
  3. C20 i +10 j +10 k 9
  4. D25 i -64 j +7 k 9

Correct answer

D. 25 i -64 j +7 k 9

Step-by-step solution

aligned & =5 i -6 j +3 k & m =4 i +2 j +4 k aligned Projection of on m is OC = m | m | OC = - m | m | m CA = - m | m | m =5 i -6 j +3 k - 20-12+12 6 4 i +2 j +4 k 6 =5 i -6 j +3 k - 5 9 (4 i +2 j +4 k )= 25 i -64 j +7 k 9

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 2026Let 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 2026Let 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 2026Let 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 2026The 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 : 2026Let 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 2026Let 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 2026Let 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 Most Important Selected Qs for JEE Advanced PYQs