The vectors a₁,a₂,....,a_n are said to be linearly dependent iff there exists real no.s l₁,l₂,....,l_n atleast one of them being non-zero,such that l₁a₁+l₂a₂+.....+l_na_n=0.Moreover,Three vectors are coplanar iff they are linearly dependent.

PLS  DO THIS SUM

If x = i + j + k , y = 4 i + 3 j + 4 k and z = i + a j + b k are linearly dependent vectors and c = , then

(1) a = 1, b = - 1

(2) a = 1, b = ± 1

(3) a = - 1, b = ± 1

(4) a = ± 1, b = 1

 

help please!

is this Q that tough??

The vectors x,y,z are linearly dependent iff they are coplanar iff

det 1 1 1  =0,on simplifying,we get b=1 and z=a²+b²=2a²=1a=1 or -1.

      4 3 4

     1 a b

Hence the ans is option 4.

[I think u might have typed c instead of z in the question]