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If the vectors vec(AB) = 3 hati + 4 hatk...

If the vectors `vec(AB) = 3 hati + 4 hatk and A vecC = 5 hati - 2 hatj + 4 hatk` are the side of the triangle ABC, then the length of the median through A is :

A

`sqrt(18)`

B

`sqrt(72)`

C

`sqrt(33)`

D

`sqrt(45)`

Text Solution

Verified by Experts

The correct Answer is:
C
We know that, the sum of three vectors of a triangle is zero.

`thereforeAB+BC+CA=0`
`implies BC=AC-AB` [`becauseAC=-CA`]
`implies AB=(AC-AB)/(2)" "[because" M is a mid-point of BC"]`
also, `AB+BM+MA=0` [by properties of a triangle]
`impliesAB+(AC-AB)/(2)=AM" "[becauseAM=-MA]`
`implies AM=(AB+AC)/(2)`
`=(3hati+4hatj+5hati-2hatj+4hatk)/(2)`
`=4hati-hatj+4hatk`
`implies|AM|=sqrt(4^(2)+1^(2)+4^(2))=sqrt(33)`.
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