wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let a, b and c be three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector a makes with vectors b and c respectively and a×(b×c)=12b, then |αβ| is equal to :

A
60
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
45
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
30
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
90
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 30
a×(b×c)=12b
(ac)b(ab)c=12b
(ac12)b(ab)c=0

As vectors b and c are non-parallel,
ac12=0
ac=12cosβ=12
​​​​​​​ β=60
and ​​​​​​​ab=0 α=90
​​​​​​​|αβ|=30

flag
Suggest Corrections
thumbs-up
28
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Linear Dependency of Vectors
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon