The equation of the plane passing through three non - collinear points with positions vectors a,b,c, is

Options

A. `r*(bxxc+cxxa+axxb)`
B. `r*(bxxc+cxxa+axxb)=["a b c"]`
C. `r*(axx(b+c))=(abc)`
D. `r*(a+b+c)=0`

Answer

B

Explanation

Let P(r) be any points on plane. Then, clearly r-a will be in linear combination of b-a and c-a
`rArr" "r-a,b-a,c-a` will be coplanar
`rArr" "(r-a)*{(b-a)xx(c-a)}=0`
`rArr" "(r-a)*{bxxc+axxb+cxxa}=0`
`=r*(bxxc+cxxa+axxb)=["a b c"]`