CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let a,b,c be non-coplanar vectors such that p=a+bc,q=b+ca,r=c+ab,d=2a3b+4c. If d=αp+βq+γr, then

A
α=γ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
α+γ=3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
α+β+γ=3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
β+γ=2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C α+β+γ=3
2a3b+4c=d=αp+βq+γr
substituting for p=a+bc,q=b+ca,r=c+ab we get
d=α(a+bc)+β(b+ca)+γ(c+ab)
By removing the coefficients of a,b and c we get
=(αβ+γ)(a)+(α+βγ)(b)+(α+β+γ)c
Comparing the left hand side with right hand side, we get
αβ+γ=2 α+βγ=3 and α+β+γ=4
αβ+γ+α+βγα+β+γ=23+4
α+β+γ=3

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Angle between a Plane and a Line
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon