If vector A=10i+49j, and vector B=vector A/2, then does vector

[k8e591]

If vector A=10i+49j, and vector B=vector A/2, then does vector B=1/2(10i+49j)?

 

[berkeman]

If vector A=10i+49j, and vector B=vector A/2, then does vector B=1/2(10i+49j)?

Yep. So how would you write out vector B then?

Welcome to the PF.

 

[k8e591]

would it be 5i+24.5j?

 

[torquil]

Yes. The main point here is that when it is written that e.g. B = A/2, it means that each component of the vector B is half the value of the corresponding component of A. The same thing goes for multiplication by a number, e.g. C = 2*A. In that case you would have C = 20i + 98j.

 

[pmacias]

Yes, vector B would equal 1/2(10i+49j) because dividing a vector by a scalar simply scales the magnitude of the original vector by the scalar value. In this case, since vector B is equal to half of vector A, its magnitude will also be half of vector A's magnitude. Therefore, the components of vector B will also be half of vector A's components, resulting in vector B=1/2(10i+49j).