    Question

# If 1,2,1 are the direction ratios of a line then the direction cosines of this line is equal to

A
26,16,16
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
16,26,16
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
16,16,26
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
16,16,16
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B 1√6,2√6,1√6We know that the direction ratios are proportional to direction cosines i.e. l= k.a, m= k.b , n= k.c where k is any constant, l ,m & n are direction cosines and a,b & c are direction ratios. We also know that l2+m2+n2=1 So,(k.a)2+(k.b)2+(k.c)2=1 k2(a2+b2+c2)=1 k2=1(a2+b2+c2) Or, k=±√1(a2+b2+c2) In the question given direction ratios or a,b,c are 1, 2, 1. So, k=±√1((1)2+(2)2+(1)2) Or, k=±√16 So the direction cosines will be - l=1.k or,l=√16(on taking k as √16) Similarly ,m=2.√16 & n=√16 Also,-√16,−2.√16,−√16 on taking k as −√16  Suggest Corrections  0      Similar questions
Join BYJU'S Learning Program
Select...  Related Videos   Direction Cosines and Direction Ratios
MATHEMATICS
Watch in App  Explore more
Join BYJU'S Learning Program
Select...