CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the measure of the angle between two lines if their direction cosines ,m,n satisfy +mn=0,2+m2n2=0.

Open in App
Solution

given ocs of two line satisfy

l + m - n = 0 equation (1)
l2+m2n2=0equation(2)

to add angle between from (1) l = n - m in equation (2)

(nm)2+m2n2=0n2+m22nm+m2n2=02m22nm=02m(mn)=0

m = 0 equation (3) and m - n = 0 equation (4)

l + m - n = 0

0 + m - n = 0

l0+1=m0=n1

l:m:n = 1 : 0 : 1
equation 1 and 4
l + m - n = 0

0 + m - n = 0
l0=m(1)=n1
l : m : n = 0 : 1 : 1

cosθ=a1a2+b1b2+c1c2a12+b12+c12a22+b22+c22

=(1)(0)+(0)(0)+(1)(1)1+0+10+1+1=12

cosθ=12θ=π2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Direction Cosines and Direction Ratios
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon