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. `5sqrt(2)`
B. `50`
C. `10sqrt(2)`
D. 10

Answer

D

Explanation

Given, `|a+b|=6`
`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`