Scalar and Vectors

Scalar

A scalar quantity only has a magnitude associated with it.

(E.g Mass, Volume, Speed, Temp)

Vectors

A vector quantity has a magnitude and a direction associated with it.

(E.g force, displacement, velocity, acceleration.)

Is it possible for two quantities to have the same dimensions but different units?

Yes they can.

Length has the dimension L

you can measure length in m, cm,in,feet etc.

is it possible for two quantities to have the same units but different dimensions?

Yes.

Torque and energy both use Newton meters, while torque is a vector quantity and energy is a scalar quantity.

Can two nonzero perpendicular vectors be added together so that their sum is zero? Explain why.

No, They form a right angle between them, so two perpendicular vectors is never zero unless both vectors are zero.

The magnitude of a vector has doubled while its direction remains the same. Has the magnitude of each component of the vector also doubled? Explain.

yes, If we double the magnitude of the vector without changing its direction, we are essentially scaling the entire vector by 2

Variable Unit x ?

distance (m)

Variable Unit v

meteres per second (m/s)

Variable Unit t

time (seconds)

Variable Unit a

Meters per second squared (m/s^2)

Is it possible for one component of a vector to be zero, while the vector itself is not zero?

yes,If one component is zero, but at least one other component is nonzero, then the vector itself is not zero.

) Is it possible for a vector to be zero, while one component of the vector is not zero? Explain.

No, if even one component is not zero, the magnitude will be greater than zero, and the vector will not be a zero vector.