The nonzero verctors ` vec a` , ` vec b` and ` vec c` are related by ` vec a=8 vec b" " and" " vec c=""-7 vec b` . Then the angle between ` vec a` and ` vec c` is

Explanation

Let `theta` be the angle between `vec(a)` and `vec(b)`.
Now , `vec(a) + vec(b) + vec( c ) = 0`
`vec(a) + vec(b) = - vec(c )`
`(vec(a) + vec(b)) . (vec(a) + vec(b)) = ( -vec( c) ) . (-vec(c ))`
`vec(a) . vec(a) + vec(b) . vec(b) + 2 vec(a) . vec(b) = vec(c ) .vec( c) [ because vec(a) . vec(b) = vec(b) . vec(a)]`
`|vec(a)|^(2) + |vec(b)|^(2) + 2 |vec(a)| |vec(b)| cos theta = |vec(c )|^(2)`
`9 + 25 + 2 (3) (5) cos theta = (7)^(2)`
`cos theta = (1)/(2) rArr theta = 60^(@)`
Hence , the angle between `vec(a)` and `vec(b) is 60^(@)`.