Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2013
Exam
BITSAT
Year
2013
Subject
Mathematics
Chapter
Three Dimensional Geometry

BITSAT 2013 · Mathematics · Three Dimensional Geometry

Find the angle between the two planes 2 x+y-2 z=5 and 3 x-6 y-2 z=7

Find the angle between the two planes 2x+y−2z=52 \mathrm{x}+\mathrm{y}-2 \mathrm{z}=5 and 3x−6y−2z=73 x-6 y-2 z=7

Options

  1. Acos⁡−1(4/21)\cos ^{-1}(4 / 21)
  2. Bcos⁡−1(2/21)\cos ^{-1}(2 / 21)
  3. Ccos⁡−1(1/21)\cos ^{-1}(1 / 21)
  4. Dcos⁡−1(5/21)\cos ^{-1}(5 / 21)

Correct answer

A. cos⁡−1(4/21)\cos ^{-1}(4 / 21)

Step-by-step solution

The angle between two planes is the angle between their normals. From the equation of the planes, the normal vectors are \overrightarrow{\mathrm{N}_{1}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}} and \overrightarrow{\mathrm{N}_{2}=3 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}} Therefore, \cos \theta=\left|\frac{\overrightarrow{\mathrm{N}_{1} \cdot \overrightarrow{\mathrm{N}_{2}}{\left|\overrightarrow{\mathrm{N}_{1}\right|\left|\overrightarrow{\mathrm{N}_{2}\right|}\right|=\left|\frac{(2 \hat{i}+\hat{j}-2 \hat{k}) \cdot(3 \hat{i}-6 \hat{j}-2 \hat{k})}{\sqrt{4+1+4} \sqrt{9+36+4}}\right|= \left(\frac{4}{21}\right)Hence, \theta=\cos ^{-1} \left(\frac{4}{21}\right)
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 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 2019 Full Three Dimensional Geometry list Three Dimensional Geometry JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs