1.

Let triangleABC be a given triangle. If |vec(BA)-tvec(BC)|ge|vec(AC)| for any t in R,then triangleABC is

Answer»

Equilateral
Right angled
Isosceles
None of these

Solution :`|vec(BA)|^(2)+t^(2)|vec(BC)|^(2)-2vec(BA).vec(BC).t-|vec(AC)|^(2)ge0 AA t in R`
Discrimiant of the quadratic equation `le0`
`rArr 4(vec(BA).vec(BC))^(2)-4|vec(BC)|^(2)|vec(BA)|^(2)+4|vec(BC)|^(2)|vec(AC)|^(2)le0`
USING `(vec(BA).vec(BC))^(2)-|vec(BC)|^(2)|vec(BA)|^(2)`
`=-|vec(BA) xx vec(BC)|^(2)`
`rArr =-|vec(CA) xx vec(BC)|^(2)`
But `|vec(AC) xx vec(BC)|=|vec(AC)||vec(BC)|SINC`
`rArr sin^(2) Cge1`
`rArr sinC=+1 rArr angleC=pi//2`


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