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+1 vote
14.7k views
in Vector algebra by (33.0k points)

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(s) 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 lies in the xy-plane, then |u1| = |u2|. 

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

1 Answer

+1 vote
by (36.3k points)
selected by
 
Best answer

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

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