Let `|bar(a)|=7, |bar(b)|=11, | bar(a)+bar(b)|=10 sqrt(3)`
What is `|bar(a)-bar(b)|` equal to ?

Options

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

Answer

B

Explanation

Let angle between `vec(a)` and `theat` .
`|vec(a)+vec(b)|=sqrt(|vec(a)|^(2)+|vec(b)|^(2)+2|vec(a)|vec(b)|cos theta|)`
`10sqrt(3)=sqrt(49xx121+2xx7xx11 cos theta)`
`300=170+154 cos theta`
`154 cos theta = 130`
`|vec(a)-vec(b)|=sqrt(|vec(a)|^(2)+|vec(b)|^(2)-2|vec(a)||vec(b)|cos theta)`
`|vec(a)-vec(b)|=sqrt(170-154cos theta)`
`|vec(a)-vec(b)|=sqrt(170-130)=sqrt(40) or 2sqrt(10)`