physics help (a few easy q's)

[moto_za]

Can someone please answer the below q's so I can check it with mine. thanks a million
Question 1
It is possible for the magnitude of a vector (select the correct answers)...

to be smaller than the magnitude of any of its components.

to be equal to the magnitude of one of its components.

Question 2
Can you find a single vector that has components different from zero, but a magnitude of zero?

Question 3
A car speedometer measures the vector quantity of velocity. True or
False

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[future_dr_house]

Question 1
It is possible for the magnitude of a vector (select the correct answers)...

to be smaller than the magnitude of any of its components. No.

to be equal to the magnitude of one of its components. Yes

Question 2
Can you find a single vector that has components different from zero, but a magnitude of zero? No

Question 3
A car speedometer measures the vector quantity of velocity. True or
False

components of vectors are in x, y, and z planes. components in one direction never affect a component in another direction (dot product is 0) and thus you can't have negative components and positive componests of one vector that makes 0 magnitude overall.

speed is a scalar, your speedometer doesn't have negative speeds right?

 

[Dave_D]

Can someone please answer the below q's so I can check it with mine. thanks a million
Question 1
It is possible for the magnitude of a vector (select the correct answers)...

to be smaller than the magnitude of any of its components.

to be equal to the magnitude of one of its components.

Question 2
Can you find a single vector that has components different from zero, but a magnitude of zero?

Question 3
A car speedometer measures the vector quantity of velocity. True or
False

The other poster answered those questions so I'll just say remember how you calculate a vector's magnitude.
2d
Mag = (X^2 + Y^2)^1/2

3d
Mag = (X^2 + Y^2 + Z^2)^1/2

In other words take each component and square them. Then add up all the numbers and take the square root. If you look at the math you can see why the answers the previous poster gave were correct when it comes to magnitude.(Well, unless you have irrational numbers but some how I doubt they're doing that🙂

 

[baylormed]

Question 1
It is possible for the magnitude of a vector (select the correct answers)...

to be smaller than the magnitude of any of its components. No.

to be equal to the magnitude of one of its components. Yes

Question 2
Can you find a single vector that has components different from zero, but a magnitude of zero? No

Question 3
A car speedometer measures the vector quantity of velocity. True or
False

components of vectors are in x, y, and z planes. components in one direction never affect a component in another direction (dot product is 0) and thus you can't have negative components and positive componests of one vector that makes 0 magnitude overall.

speed is a scalar, your speedometer doesn't have negative speeds right?

For question #2, if you have a vector whose components are opposed in a 180* fashion, and are both of the same magnitude...wouldn't the resulting vector be equal to zero?

I forgot my physics already, so I might just be very wrong, but I seem to think it is possible.

 

[Soggun]

Could be wrong, but I think a vector can only have 1 component for each dimension (x,y, and z). Let's say for example that the y and z components are both 0, then the x component could be positive or negative, but either way, it's magnitude would be equal to that of the x componant. If the x componant was 0 also, the vector would no longer exist. As I said though, been awhile - could be wrong.

 

[Mr. Tee]

For question #2, if you have a vector whose components are opposed in a 180* fashion, and are both of the same magnitude...wouldn't the resulting vector be equal to zero?

I forgot my physics already, so I might just be very wrong, but I seem to think it is possible.

components are x-components and y-components (or z-components). what I bolded cannot happen as a consequence. Since the formula is magnitude = sqrt(x^2+y^2+z^2), directionality of the components doesn't matter, and magnitude will always be equal or greater than one of its components.

 

[future_dr_house]

For question #2, if you have a vector whose components are opposed in a 180* fashion, and are both of the same magnitude...wouldn't the resulting vector be equal to zero?

I forgot my physics already, so I might just be very wrong, but I seem to think it is possible.

those wouldn't be components of a single vector, you are thinking of two different vectors whose magnitude sum to 0.

if we are dealing with only one vector and it's components, then there is not a way the total magnitude could be 0 if any of the components is not 0

 

[dannylee718]

you nerds. all the answers from the first reply are correct.
for Q3, its not a vector because vectors need both magnitude and angle (direction).

post another physics Q. i'm bored.

 

[future_dr_house]

Could be wrong, but I think a vector can only have 1 component for each dimension (x,y, and z). Let's say for example that the y and z components are both 0, then the x component could be positive or negative, but either way, it's magnitude would be equal to that of the x componant. If the x componant was 0 also, the vector would no longer exist. As I said though, been awhile - could be wrong.

👍

 

[Mr. Tee]

for Q3, its not a vector because vectors need both magnitude and angle (direction).

Stop joking.

 

[deleted103644]

Haha, the first reply got all the answers right, but here's a twist... You CAN have a zero magnitude vector, just not in R^3. In a minkowski space like space-time in special relativity, the magnitude of a vector is x^2 + y^2 + z^2 - c^2 t^2 (sqrt). So the magnitude of any vector connecting two points in space-time that can be connected by a ray of light is actually 0. I actually may have set up that magnitude equation wrong, it may be reversed, but that doesn't matter that much. Just switches which values will be imaginary or real, light paths will always be 0.