# Extremely Difficult Unit Vector Question?

Select the correct answer for each of the four questions; e.g., if A is correct for question (i), and B is correct for questions (ii), (iii), and (iv), enter ABBB. (i) Consider the vector A  =  3î, and any non-zero vector B such that A×B  =  0. A. The vector B must be in the y-z plane. B. The vector B must... show more Select the correct answer for each of the four questions; e.g., if A is correct for question (i), and B is correct for questions (ii), (iii), and (iv), enter ABBB.

(i) Consider the vector A  =  3î, and any non-zero vector B such that A×B  =  0.

A. The vector B must be in the y-z plane.
B. The vector B must be parallel to î.
C. The vector B must be parallel to k.
D. None of the three statements above is true.

(ii) Assume C  =  2î. Which of the following statements is true?

A. If D  =  (1/2)ĵ, then C×D  =  1k.
B. If D  =  −2k, then C×D  =  −4î.
C. If D  =  (−5/2)î, then C×D  =  5ĵ.
D. None of the three statements above is true.

(iii) Consider the vector E  =  1ĵ, and any non-zero vector F such that E·F  =  0.

A. The vector F must be in the x-y plane.
B. The vector F must be in the y-z plane.
C. The vector F must be in the x-z plane.
D. None of the three statements above is true.

(iv) Consider the vector G  =  4ĵ. Which of the following vectors H satisfies G·H  =  1 ?

A. H  =  (1/4)î.
B. H  =  (1/4)î+ĵ+k.
C. H  =  î+(1/4)ĵ+k.
D. H  =  î+ĵ+(1/4)k.
E. H  =  î+ĵ+k.