Mathematics

Problem

Two vectors

\vec A

and

\vec B

each have magnitude

4\,\text{units}

. A measurement gives their dot product as

-0.10\,\text{unit}^2

with an instrumental uncertainty of

\pm0.05\,\text{unit}^2

. Which of the following statements best describes the orientation of

\vec A

with respect to

\vec B

? a) They must be anti-parallel (angle

180^{\circ}

). b) The angle between them is less than

30^{\circ}

. c) The given uncertainty is too large to determine their relative orientation. d) They are nearly perpendicular to each other.