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

Let a,b,c be three unit vectors such that a+b+c=0. If λ=a.b+b.c+c.a and d=a×b+b×c+c×a, then the ordered pair λ,d is


A

32,3a×c

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

-32,3c×b

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

-32,3a×b

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

32,3b×c

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

-32,3a×b


Explanation for correct option:

Finding the ordered pair:

a,b,c be three unit vectors. [Given]

a=b=c=1.

Since, a+b+c=0, we get,

a+b+c.a+b+c=0a.a+a.b+a.c+b.a+b.b+b.c++c.a+c.b+c.c=0a2+b2+c2+2(a.b+b.c+c.a)=01+1+1+2(a.b+b.c+c.a)=0[a=b=c=1]3+2λ=0[λ=a.b+b.c+c.a]λ=-32

Calculating the value of d

d=a×b+b×c+c×a=a×b+b×-a-b+-a-b×a[a+b+c=0]=a×b+b×-a-b×b-a×a)+(-b×a=a×b-b×a-b×a[a×a=0]=a×b+a×b+a×b[a×b=-b×a]=3a×b

Therefore, the ordered pair λ,d is -32,3(a×b.

Hence, option (C) is the correct answer.


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