Question

$\bigstar \large \purple{\pmb{ \sf question}}$

$\sf \overrightarrow{A}$ with maginitude 3kg m/s points in the N-E direction. It is multiplied by a scalar l such that l = -4 second. Find the direction and magnitude of the new vector quantity. Does it represent the same physical quantity of not !?

Kinda puzzled :D
So, try to mention all the steps !

Have a great answering time ✌️​

Answer 1

Question:

$\sf \overrightarrow{A}$ with maginitude 3kg m/s points in the N-E direction. It is multiplied by a scalar l such that l = -4 second. Find the direction and magnitude of the new vector quantity. Does it represent the same physical quantity of not !?

Solution:

A vector A is multiplied by a scalar I = - 4 second.

Magnitude of A= 3kg m/s (N-E direction)

After multiplying a vector by a scalar, the direction of vector won't change, it will just affect the magnitude. When a vector is multiplied by a negative scalar, the direction will be reversed.

But, time cannot be negative, how it is given I = - 4second???

And it's obvious that if you multiply a vector with a scalar, the physical quantity will change.

For example, when we multiply acceleration vector with mass which is a scalar, we get another physical quantity Force.

Now you deal with your question yourself.

Answer 2

Given :-

$\sf \overrightarrow{A}$ with maginitude 3kg m/s points in the N-E direction. It is multiplied by a scalar l such that l = -4 second.

To Find :-

Find the direction and magnitude of the new vector quantity. Does it represent the same physical quantity or not !?

Solution :-

As the scalar quantity is multiplied by $\sf \overrightarrow{A}$ To get a new vector quantity .

So , Let the new vector quantity ( resulting ) = $\sf \overrightarrow{R}$

So , The magnitude of $\sf \overrightarrow{R}$ will equal to the product of magnitude of l and $\sf \overrightarrow{A}$ i.e :-

[ Because , it is given that $\sf \overrightarrow{R}$ ( The resulting quantity ) is formed after Multiplying I and $\sf \overrightarrow{A}$ ] .

-4 s × 3 kg m/s

=> 3 × -4 kg m/s × s

=> -12 kg . m

Note that the magnitude of $\sf \overrightarrow{R}$ is -12 kg.m neither -12 kg m/s nor -12 kg / m

Now , The signs of the magnitude are opposite . So , The resulting vector will point the direction i.e opposite to North - East Direction i.e South - West .

And , It doesn't represent the same physical quantity !