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Let triangleABC be a given triangle. If ...

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

A

Equilateral

B

Right angled

C

Isosceles

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`|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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