If a and b are two vectos such that `a.b lt 0 and |a.b|=|axxb|`, then the angle between a and b is

Options

A. `(3pi)/(4)`
B. `(2pi)/(3)`
C. `(pi)/(4)`
D. `(pi)/(3)`

Answer

A

Explanation

Given, `|a *b| = | axxb| `
` rArr |a||b||cos theta|=|a||b||sin theta|`
[ where, `theta` is the angle between a and b]
`rArr |cos theta| = |sin theta| `
`rArr theta = (pi)/(4) or (3pi)/(4) " " [ "as " 0 le theta le pi ]`
But `a*b lt 0 `
`therefore theta =(3pi)/(4) `