Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Three Dimensional Geometry

BITSAT 2023 · Paper 1 · Mathematics · Three Dimensional Geometry

The ratio in which the YZ-plane divide the line segment formed by...

The ratio in which the YZ-plane divide the line segment formed by joining the points (−2,4,7)(-2,4,7) and (3,−5,8)(3,-5,8) is 2:m2: \mathrm{m}. The value of m\mathrm{m} isThe ratio in which the YZ-plane divide the line segment formed by joining the points (-2,4,7) and (3,-5,8) is 2: m .

Options

  1. A2
  2. B3
  3. C4
  4. D1

Correct answer

B. 3

Step-by-step solution

Let the points be A(−2,4,7)andB(3,−5,8)A(-2,4,7) and B(3,-5,8) on YZY Z-plane, xx-coordinate =0=0.
The ratio in which the YZ-plane divide the line segment formed by joining the points (-2,4,7) and (3,-5,8) is 2: m .

Let the ratio be K:1K: 1.
The coordinates of CC are \left(\frac{3 K-2}{K+1}, \frac{-5 K+4}{K+1}, \frac{8 K+7}{K+1}\right)<br/>Clearly<br />Clearly\frac{3 K-2}{K+1}=0 \Rightarrow 3 K=2 \Rightarrow K=\frac{2}{3}<br/>Hencerequiredratiois<br />Hence required ratio is2: 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 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 distance from the point (3,4,5) to the point where the line… BITSAT 2020The 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