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Consider three vectors vec(A)=2 hat(i)...

Consider three vectors
`vec(A)=2 hat(i)+3 hat(j)-2 hat(k)" " vec(B)=5hat(i)+nhat(j)+hat(k)" " vec(C)=-hat(i)+2hat(j)+3 hat(k)`
If these three vectors are coplanar, then value of n will be

A

0

B

12

C

16

D

18

Text Solution

Verified by Experts

The correct Answer is:
D
For coplanar vectors `vec(A).(vec(B)xxvec(C))=|(A_(x),A_(y),A_(z)),(B_(x),B_(y),B_(z)),(C_(x),C_(y),C_(z))|=0`
`implies |(2,3,-2),(5,n,1),(-1,2,3)|=2(3n-2)-3(15+1)-2 (10+n)=0 implies4n-72=0implies n=18`
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