If r `a=r. b=r. c=1` where a, b, c are any three non-coplanar vectors, then r is

Options

A. coplanar with a, b, c
B. parallel to `a+b+c`
C. parallel to `b xx c+c xx a+axxb`
D. parallel to `(a xx b) xx c`

Answer

C

Explanation

Now,l `r*a=r*b`
`implies r((a-b)=0`
Similarly, `r*(b-c)=0`
Since, r is parallel to `(a-b)xx(b-c).`
So, r is parallel to `axx b +c xx a +b xx c`