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प्रश्न
The two vectors `hatj+hatk " and " 3hati-hatj+4hatk` represent the two sides AB and AC, respectively of a ∆ABC. Find the length of the median through A
उत्तर
In ∆ABC,
Using the triangle law of vector addition, we have
`vec(BC)=vec(AC)-vec(AB)`
`=(3hati-hatj+4hatk)-(hatj+hatk)`
`=3hati-2hatj+3hatk`
`:.vec(BD)=1/2vec(BC)=3/2hati-hatj+3/2hatk " (Since AD is the median)"`
In ∆ABD, using the triangle law of vector addition, we have
`vec(AD)=vec(AB)+vec(BD)`
`=(hatj+hatk)+(3/2hati-hatj+3/2hatk)`
`=3/2hati+0hatj+5/2hatk`
`:.AD=sqrt((3/2)^2+0^2+(5/2)^2)=1/2sqrt34`
Hence, the length of the median through A is `1/2sqrt34`units.
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