1.

दर्शाइए कि बिंदु `A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)` और `C(7hati-hatk)` संरेख है।

Answer» `vec(AB)=(1+2)hati+(2-3)hatj+(3-5)hatk=3hati-hatj-2hatk`
`vec(BC)=(7-1)hati+(0-2)hatj+(-1-3)hatk=6hati-2hatj-4hatk`
`vec(AC)=(7+2)hati+(0-3)hatj+(-1-5)hatk=9hati-3hatj-6hatk`
`|vec(AB)|=sqrt(14),|vec(BC)|=2sqrt(14)` and `|vec(AC)|=3sqrt(14)`
इसलिए `|vec(AC)|=|vec(AB)|+|vec(BC)|`
अतः बिंदु `A,B,C` संरेख है।


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