wiz-icon
MyQuestionIcon
MyQuestionIcon
13
You visited us 13 times! Enjoying our articles? Unlock Full Access!
Question

For non-zero vectors a,b,c;(a×b)c=abc holds if and only if

A
ab=0,bc=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
bc=0,ca=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
ca=0,ab=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
ab=bc=ca=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is C ab=bc=ca=0
We have (a×b)c=abc
absinθ^nc=abc
abcsinθcosα=abc
|sinθ||cosα|=1
θ=π2 and α=0
ab and c is parallel to ^n
ab and c to both a and b
a, b, c are mutually perpendicular
ab=bc=ca=0
Hence (D) is correct.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Basic Operations
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon