If `bar a,bar b and bar c` are perpendicular ,`bar c+bar a, bar b+bar c and bar a+bar b` +respectively and if `|bar a+bar b|=6,|bar b+bar c|=8 and |bar c+bar a|=10` , then `|bar a+bar b+bar c|` is equal to

Options

A. `5sqrt2`
B. `50`
C. `10sqrt2`
D. 10

Answer

D

Explanation

Given `|a|^(2)+|b|^(2)+2 a*b=36" "...(i)`
Similarly, `|b|^(2)+|c|^(2)+2b*x=64" "...(ii)`
`and |c|^(2)+|a|^(2)+2c*a=100" "...(iii)`
If a, b and c are perpendicular to `b+c,c+a and a+b` respectively, then
`a*b+b*c+c*a=0" "..(iv)`
On edding Eqs. (i),(ii),and (iii), we get
`|a|^(2)+|b|^(2)|+|c|^(2)+`
`2(a*b+b(c+c*a)=100`
`implies|a|^(2)+|b|^(2)=100" "...(v)`
Now `|a+b+c|^(2)=|a|^(2)+|b|^(2)+|c|^(2)`
`implies|a+b+c|^(2)=100`
`implies|a+b+c|=10`