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

If a=^i+^j^k,b=^i^j+^k, and c is unit vector perpendicular to the vector a and coplanar with a and bthen a unit vector d perpendicular to both a and c, is

A
16(2^i^j+^k)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
12(^j+^k)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
12(^i+^j)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
12(^i+^k)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 12(^j+^k)
We have, c=±a×(a×b)|a×(a×b)|
Now, a×(a×b)=(a.b)a(a.a)b
=^i^j+^k3(^i^j+^k)=4^i+2^j2^kc=±16(2^i^j+^k)
Since, d is a unit vector perpendicular to both a and c
Therefore, d=±a×c|a×c|
Now, a×c=±16∣ ∣ ∣^i^j^k111211∣ ∣ ∣=±16(3^j3^k)
d=±12(^j^k)=±12(^j+^k)

flag
Suggest Corrections
thumbs-up
8
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Applications of Cross Product
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon