Question

If b and c are any two perpendicular unit vectors and a is any vector, then (a.b)b + (a.c)c + (a .(b x c))/|b x c|(b x c) =

(A) b 

(B) a 

(C) c 

(D) b + c

Answer 1

Answer is (B) a

Consider three non-coplanar vectors b, c and b × c. Any vector a can be written as

a = xb + yc + z(b x c)     (1)

aking dot product with b c × in Eq. (1), we get

Taking dot product with b in Eq. (1), we get

a.b = xb.b + yc.b + z. 0 = x

Taking dot product with c in Eq. (1), we get

a.c = y

Thus,