If `|vec(a)|=3, |vec(b)|=4 and |vec(a)-vec(b)|=5`, then what is the value of `|vec(a)+vec(b)|=?`

Options

A. 3
B. 2
C. 1
D. 0

Answer

C

Explanation

Given, `|vec(a)|=3, |vec(b)|=4 and |vec(a)-vec(b)|=7`
Since, `|vec(a)+vec(b)|^(2)+|vec(a)-vec(b)|^(2)=2[|vec(a)|^(2)+|vec(b)|^(2)]`
`:.` By putting the values of `|vec(a)|, |vec(b)| and |vec(a)-vec(b)|` we get
`|vec(a)+vec(b)|^(2)+7^(2)=2[3^(2)+4^(2)]`
`|vec(a)+vec(b)|^(2)=50-49 rArr |vec(a)+vec(b)|^(2)=1 rArr |vec(a)+vec(b)|=1`