question_answer

If \[\vec{a}=\hat{i}+\hat{j}+\hat{k},\,\,\vec{b}=4\hat{i}+3\hat{j}+4\hat{k}\] and \[\vec{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k}\] are linearly dependent vectors and \[|\vec{c}|=\sqrt{3}\], then

A)  \[\alpha =1,\text{ }\beta =-1\]                        

B)  \[\alpha =1.\text{ }\beta =\pm \text{ }1\]

C)  \[\alpha =-1,\beta =\,\pm \,1\]    

D)                   \[=f(k)-F(1)\]