Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Mathematics
Chapter
Three Dimensional Geometry

BITSAT 2020 · Mathematics · Three Dimensional Geometry

The distance from the point (3,4,5) to the point where the line...

The distance from the point (3,4,5) to the point where the line x−31=y−42=z−52\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2} meets the plane x+y+z=17x+y+z=17 is

Options

  1. A1
  2. B2
  3. C3
  4. D2\sqrt{2}

Correct answer

C. 3

Step-by-step solution

Anypoint on the line is (r+3,2r+4,2r+5)(r+3,2 r+4,2 r+5). It lies on the plane x+y+z=17∴(r+3)+(2r+4)+(2r+5)=17x+y+z=17\therefore(r+3)+(2 r+4)+(2 r+5)=17 i.e r=1r=1 Thus the point of intersection of the plane and the line is (4,6,7) Required distance = distance between (3,4,5) and (4,6,7) ={(4−3)2+(6−4)2+(7−5)2}=3=\sqrt{\left\{(4-3)^{2}+(6-4)^{2}+(7-5)^{2}\right\}}=3
Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

The magnitude of projection of line joining (3,4 , 5) and (4,6,3) on the line joining… BITSAT 2024The angle between the lines whose direction cosines are given by the equations 3 l+m+5… BITSAT 2024Let the acute angle bisector of the two planes x-2 y-2 z+1=0 and 2 x-3 y-6 z+1=0 be the… BITSAT 2024Let the foot of perpendicular from a point P(1,2,-1) to the straight line L: x 1 = y 0 =… BITSAT 2024If the co-ordinates of the point in which the line joining the points (3,5,-7) and… BITSAT 2023If the straight lines (x-1)/(k)=(y-2)/(2)=(z-3)/(3) and (x-2)/(3)=(y-3)/(k)=(z-1)/(2)… BITSAT 2023The shortest distance between the lines x=y+2=6 z-6 and x+1=2 y=-12 z is BITSAT 2023The ratio in which the YZ-plane divide the line segment formed by joining the points… BITSAT 2023The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)/(1) are coplanar if BITSAT 2023The shortest distance between the lines (x-3)/(2)=(y-2)/(3)=(z-1)/(-1) and… BITSAT 2023If the plane 3 x+y+2 z+6=0 is parallel to the line (3 x-1)/(2 b)=3-y=(z-1)/(a) , then the… BITSAT 2022The length of the perpendicular drawn from the point (3,-1,11) to the line… BITSAT 2021A line makes angles of 45^ ^ ∘ and 60^ ^ ∘ with the positive axes of X and Y… BITSAT 2021The equation of plane containing line x - y = 1, z = 1 and parallel to (x)/(2) - (z)/(3)… BITSAT 2019The angle between the lines whose direction cosine satisfy the equations l + m + n = 0… BITSAT 2019An equation of plane parallel to plane x - 2y + 2z - 5 = 0 and at a unit distance from… BITSAT 2019 Full Three Dimensional Geometry list Three Dimensional Geometry JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs