1.

vec(a) , vec(b), vec(c ) are three vectors of which every pair is non collinear. If the vector vec(a)+vec(b) and vec(b)+vec(c ) are collinear with vec(c ) and vec(a) respectively then vec(a) + vec(b) + vec(c ) is :-

Answer»

Unit vector
A NULL vector
Equally inclined to `vec(a), vec(B), vec(c )`
None

Solution :`bar(a) + bar(b) = t_(1) bar(c )`
`implies bar(a) + bar(b) + bar(c ) = (t_(1)+1) bar(c )` ……..(i)
`bar(b)+bar(c )=t_(2) bar(a)`
`implies bar(a) + bar(b) + bar(c ) = (t_(2)+1) bar(a)` ……..(ii)
from (i) and (ii)
`(t_(1)+1) bar(c )=(t_(2)+1)bar(a)`
but `bar(a) and bar(c )` are non-collinear
`:. t_(1) + 1 = t_(2) + 1 = 0`
`implies t_(1) = t_(2) = -1`
PUT `t_(1) = -1` in (i)
`bar(a) + bar(b) + bar(c ) = 0`.


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