Vector representing physical quantity?

Question

this is for homework,

Suppose we have a vector representing some physical quantity. Will the numerical value of the magnitude change if we express it in different units?

can you please explain your answer as best as you can

Answer 1

SCALER VECTOR =ONLY RESPESTED MAGNITUDE=DOT PRODUCT=MASS ,SPEED,LENTH

VECTOR PRODUCT=DIRECTION AND MAGNITUTE=CROSS PRODUCT=ACCESATION,VELOCITY,ANGULAR MOMENTUM

R2=A2+B2+2A*B*COS[DIGREE]=SCALER

R2=A2+B2+2A*B*SIN[DIGREE]NULL VECTOR=VECTOR  

Answer 2

The numbers will change using different units of course but the value won't change. If you convert back to the original units you will have the original number. It's like money. I can express a given amount in different units. Say I have $1.50. If I use cents as a unit I have 150 cents. If i use dollars as the unit I have 1.5 dollars. They both mean the same thing. The value doesn't change. The value is the magnitude. Expressing it in different units does not change the magnitude.

Answer 3

Lets say your vector is a velocity vector; you are moving 27 m/s north. Your magnitude is 27 m/s, and your direction is north.

By switching only units, we could say that you're moving 60 miles per hour north. It is the same exact physical velocity, but the magnitude of the vector has changed because the units have changed.

Answer 4

it depends on the units that you want to express it in and the conversion factor

Answer 5

The magnitude "size" of the vector does not change

The number will change, but the magnitude is the same

via conversion.

Example: displacement

let's try kilometers:

vector=10(km)i+5(km)j

magnitude=sqr(10^2+5^2) = 11.18033 kilometers

since: 1 kilometer = 1000 meters

let's try again using meters:

vector=10000(m)i+5000(m)j

magnitude=sqr(10000^2+5000^2) = 11180.33 meters

but

11180.33 meters = 11.18033 kilometers

So, the actual distance "magnitude" traveled does

not change