The number of integral values of p for which `(p+1) hati-3hatj+phatk, phati + (p+1)hatj-3hatk` and `-3hati+phatj+(p+1)hatk` are linearly dependent vectors is q

The number of integral values of p for which `(p+1) hati-3hatj+phatk,

1.	The number of integral values of p for which `(p+1) hati-3hatj+phatk, phati + (p+1)hatj-3hatk` and `-3hati+phatj+(p+1)hatk` are linearly dependent vectors is q
Answer» Correct Answer - B The vectors are linearly dependent `rArr \|{:(p+1,-3,p),(p,p+1,-3),(-3,p,p+1):}\|=0` `rArr (2p-2)\|{:(1,-3,p),(1,p+1,-3),(1,p,p+1):}\|=0` `rArr 2(p-1)\|{:(1,-3,p),(0,p+4,-3-p),(0,p+3,1):}\|=0` `rArr 2(p-1)(p+4)+(p+3)^(2)=0` `rArr (p-1)(p^(2)+7p+13)=0` Roots of `p^(2)+7p+13=0` are (imaginary) `therefore p=1` Only integral value of p is 1.