Saved Bookmarks
| 1. |
If a, b and c are perpendicular to b+c, c+a and a+b respectively and if |a+b|=6, |b+c|=8 and |c+a|=10, then |a+b+c| is equal to |
|
Answer» `5sqrt(2)` `RARR""|a|^2+|b|^2+2a*b=36"…(i)"` Similariy,`|b|^2+|c|^2+2b*c=64"…(ii)"` and`|c|^2+|a|^2+2c*a=100"…(iii)"` On adding Eqs. (i), (ii) and (iii), we GET `2[|a|^2+|b|^2+|c|^2+(a*b+b*c+c*a)]=200` `rArr""|a|^2+|b|^2+|c|^2=100"...(IV)"[because a*b+b*c+c*a=0]` Now, `|a+b+c|^2=|a|^2+|b|^2+|c|^2+2(a*b+b*c+b*a=0)` `rArr""|a+b+c|^2=100"[from EQ.(iv)]"` `rArr""|a+b+c|=10` |
|