Question

Select the correct answer.
(At first I believed it was BCBC but it seems I am wrong)

Answer 1

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

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

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

A)If D = (5/2)ĵ, then C×D = 5k hat.
B)If D = (−1/2)k hat, then C×D = −1î.
C)If D = (−3/2)î, then C×D = 3ĵ.
D)None of the three statements above is true.

(iii) Consider the vector E = 5î, 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 = 5ĵ. Which of the following vectors H satisfies G·H = 1 ?

A)H = (1/5)î.
B)H = (1/5)î+ĵ+k hat.
C)H = î+(1/5)ĵ+k hat.
D)H = î+ĵ+(1/5)k hat.
E)H = î+ĵ+k hat.