Question

The linear relation between ā= -3I - 2j - 4k b=i +i -2k,c = 2i + j+ 3k is​

Answer 1

Step-by-step explanation:

clear out the question ok

Answer 2

Given: The vectors ā= -3i - 2j - 4k , b=i +j -2k and

c = 2i + j+ 3k

To find: Linear relation between them

Solution: For finding the relation between these three vectors,

Let a = kb + tc --- equation (i)

where k and c are any constants.

Therefore, putting values of vectors:

-3i - 2j - 4k = k(i +j -2k) + t(2i + j+ 3k)

Equating vector i,

-3 = k+2t --- equation (ii)

Equating vector j,

-2 = k +t ----equation (iii)

Subtracting equation (iii) from equation (ii):

-3-(-2) = k+2t-(k+t)

=> -3+2 = k+2t-k-t

=> -1 = t

Putting t= -1 in Equation (iii),

-2 = k -1

=> k = -2+1

=> k = -1

Putting k=t= -1 in Equation (i)

a = -1(b) -1(c)

=> a = -b-c

=> a + b +c = 0

Therefore, the linear relation between them is a+b+c=0.