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

If a and b are perpendicular unit vectors and vector c is such that c=a+b, then (a×b).(b×c)+(b×c).(c×a)+(c×a).(a×b) is

A
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
-1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
b.c+c.a
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C -1
(a×b).(b×c)+(b×c).(c×a)+(c×a).(a×b)
=(a.b)(b.c)(a.c)(b.b)+(b.c)(c.a)(b.a)(c.c)+(c.a)(a.b)(c.a)(a.b)(a.a)
=0(a.c)+(b.c)(c.a)0+0(c.b)(a.b=0)
=(b.c)(c.a)(c.a)(b.c)+11
=((b.c)1)((c.a)1)1
=(11)(11)1=1(c=a+b)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
The Work Done as a Dot-Product
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon