Fundamentals of Physics Test Bank questions?

[Ishida52134]

Homework Statement

We say that the displacement of a particle is a vector quantity. Our best justification for this assertion is:
A. displacement can be specified by a magnitude and a direction
B. operating with displacements according to the rules for manipulating vectors leads to results
in agreement with experiments
C. a displacement is obviously not a scalar
D. displacement can be specified by three numbers
E. displacement is associated with motion

If the x component of a vector A, in the xy plane, is half as large as the magnitude of the
vector, the tangent of the angle between the vector and the x-axis is:
A. √3
B. 1/2
C. √3/2
D. 3/2
E. 3

The Attempt at a Solution

I'm pretty sure the answers are supposed to be A and A.
However the answer key states that it's B and D.
Is it wrong?

 

[Saitama]

For any quantity to be a vector quantity, it should follow laws of vector addition.

Show your attempt for the second question.

 

[Ishida52134]

it's just 30 60 90 triangle. ratio is x xrt 3 and 2x. tan 60 = x rt 3 / x = rt 3.
I just want to know if the answer key is wrong.
Well yeah, in order for it to be a vector space it has to fulfull rules of addition and scalar multiplication.
But the the definition of a vector quantity is that it has direction in addition to magnitude. Why would B be a better justification than A?

 

[Ishida52134]

any ideas?
for the first one, is it because vectors don't necessarily have to have direction in all cases? Like when you have tensors, with m=2, where you have bivectors, or pseudovectors?
But they all have to agree under the conditions of a vector space?

 

[Ishida52134]

any ideas

 

[TSny]

You are correct that the answer to the second question is A.

For the first question, you often see "vector" as used in physics to be defined simply as any quantity that has both a magnitude and a direction. However, a more complete definition includes the additional requirement that the quantity obeys the vector law of addition (as pointed out by Pranav-Arora).

 

[Ishida52134]

ok thanks.