Question

54. If (k,3,1) is a linear combination of vectors (3,2,1) and (2,1,0) in R3, then the value of k is
(A) 2
(B) 3
(C) 5
(D) 7

Answer 1

Answer:

(A) 2 then value of k vectors

Answer 2

Answer:

The correct answer for the value of k in the given problem is the option c) 5.

Step-by-step explanation:

Linear combination of a number of vectors is the linear sum of the given vectors. For example: Let's say that the vector $\overline c \ [x,y,z]$ is the linear combination of the vectors $\overline a \ [x_1,y_1,z_1]$ and $\overline b \ [x_2,y_2,z_2]$, then:

$\overline c \ [x,y,z]=\overline a \ [x_1,y_1,z_1]+\overline b \ [x_2,y_2,z_2]$

So, we can say that:

$x=px_1+qx_2\\y=py_1+qy_2\\z=pz_1+qz_2$

The given problem also satisfies the above relation as:

$3=2+1$   for y-coordinates

$1=1+0$   for z-coordinates

Using this in the given problem, we can say:

$k=3+2$

$k=5$

Thus, the missing value of k is found to be 5.