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If the vectors 6hati-2hatj+3hatk, 2hat...

If the vectors `6hati-2hatj+3hatk, 2hati+3hatj-6hatk and 3hati+6hatj-2hatk` form a triangle, then it is

A

right angled

B

obtuse angled

C

equilateral

D

isosceles

Text Solution

Verified by Experts

The correct Answer is:
B
AB=Position vectors of B positionn vector of A
`=(2hati+3hatj-6hatk)-(6hati-2hatj+3hatk)=-4hati+5hatj-9hatk`
`implies|AB|=sqrt(16+25+81)=sqrt(122)`
`BC=hati+3hatj+4hatk`
`implies|BC|=sqrt(1+9+16)=sqrt(26) and AC=-3hati+8hatj-5hatk`
`implies|AC|=sqrt(98)`
therefore, `AB^(2)=122,BC^(2)=26 and AC^(2)=98`
`impliesAB^(2)+BC^(2)=26+122=148`
Since, `AC^(2) lt AB^(2)+BC^(2)`, therefore `DeltaABC` is an obtuse angled triangle.
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