Question

Let u = u1i + u2j + u3k be a unit vector in R3 and vector w = (1/√6)(i + j + k). Given that there exists a vector v in R3 such that |vector(u × v)| = 1 and w. vector(u × v) = 1.

Which of the following statement(*) is(are) correct?

(a) There is exactly one choice for such vector v.

(b) There are infinitely many choices for such vector v.

(c) If vector u **** in the xy-plane, then |u1| = |u2|.

(d) If vector u **** in the xz-plane, then 2|u1| = |u3|.

Answer 1

We have,

As it is given that there exists a vector v.

w must be perpendicular to u

Hence, infinitely many such vectors v exist.

If