Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Mathematics
Chapter
Three Dimensional Geometry

BITSAT 2012 · Mathematics · Three Dimensional Geometry

What is the value of n so that the angle between the lines having...

What is the value of nn so that the angle between the lines having direction ratios (1,1,1)and(1,−1,n)and (1,-1, n) is 60∘?60^{{}^{\circ}} ?

Options

  1. A3\sqrt{3}
  2. B6\sqrt{6}
  3. C3
  4. DNone of these

Correct answer

B. 6\sqrt{6}

Step-by-step solution

If (l1,m1,n1)\left(l_{1}, m_{1}, n_{1}\right) and (l2,m2,n2)\left(l_{2}, m_{2}, n_{2}\right) are the direction ratios then angle between the lines is cos⁡θ=l1l2+m1m2+n1n2l12+m12+n12l22+m22+n22\cos \theta=\frac{l_{1} l_{2}+m_{1} m_{2}+n_{1} n_{2}}{\sqrt{l_{1}^{2}+m_{1}^{2}+n_{1}^{2}} \sqrt{l_{2}^{2}+m_{2}^{2}+n_{2}^{2}}} Here l_{1}=1, m_{1}=1, n_{1}=1 and l2=1,m2=−1,n2=nandθ=60∘∴cos⁡60∘=1×1+1×(−1)+1×nh2+12+12×12+12+y2⇒12=132+n2⇒3(2+n2)=4n2⇒n2=6⇒n=±6l_{2}=1, m_{2}=-1, n_{2}=n and \theta=60^{{}^{\circ}}\therefore \cos 60^{{}^{\circ}}=\frac{1 \times 1+1 \times(-1)+1 \times n}{\sqrt{h^{2}+1^{2}+1^{2} \times} \sqrt{1^{2}+1^{2}+y^{2}}}\Rightarrow \frac{1}{2}=\frac{1}{\sqrt{3} \sqrt{2+n^{2}}} \Rightarrow 3\left(2+n^{2}\right)=4 n^{2}\Rightarrow n^{2}=6 \Rightarrow n=\pm \sqrt{6}
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