1.

If the vectors phati+hatj+hatk, hati, qhatj+hatk and hati+hatj+rhatk(p ne q ne r ne1) are coplanar, then the value of pqr-(p+q+r) is

Answer»

`-2`
2
0
`-1`

SOLUTION :Let `a = phati+ hatj + HATK, b = HATI +hatj + hatk` andc = `hati + hatj + rhatk`are coplanar and `( p ne q ne R ne 1)`.
Since, a, b and c are coplanar .
`:. [a,b,c]= 0 rArr |{:(p,1,1),(1,q,1),(1,1,r):}| = 0`
`rArr p(qr- 1) - 1 (r-1) + 1 (1-q) = 0`
`rArr PQR - p -r + 1 + 1-q = 0`
`:. pqr - (p+q+r) = - 2`


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