- 1,233

- 1

Just had some general questions, and some more specific problems regarding vectors:

1. Can a vector be zero if one of its components is not zero? Let us assume that

2. Name some scalar quantities. Is the value of a scalar quantity dependent on the reference frame chosen? I am choosing temperature as a scalar quantity. I dont think the reference frame matters because you can convert between systems.

3. We can order events in time. There can be a time order between three events a,b,c. Is time a vector then? It has a magnitude, but I would not say a direction because even scalar quantities can be "ordered." Is this correct?

4. Two vectors

5. If we have two vectors

Any help is appreciated

Thanks

1. Can a vector be zero if one of its components is not zero? Let us assume that

**r = a+b**. Then [itex] r_{x} = a_{x} + b_{x} [/itex] and [itex] r_{y} = a_{y}+b_{y} [/itex]. So [itex] r = \sqrt{r_{x}^{2} + r_{y}^{2}} [/itex]. I'm guessing that both components have to be 0, so that [itex] 0 = \sqrt{r_{x}^{2} + r_{y}^{2}} [/itex]2. Name some scalar quantities. Is the value of a scalar quantity dependent on the reference frame chosen? I am choosing temperature as a scalar quantity. I dont think the reference frame matters because you can convert between systems.

3. We can order events in time. There can be a time order between three events a,b,c. Is time a vector then? It has a magnitude, but I would not say a direction because even scalar quantities can be "ordered." Is this correct?

4. Two vectors

**a**and**b**are added. Show that the magnitude of the resultant cannot be greater than*a+b*or smaller than |*a-b*|. Wouldnt I just use the triangle inequality theorem in which the sum of any two sides has to be greater than the third side, and the difference of any two sides has to less than the third side?5. If we have two vectors

**a**and**b**then when (a)**a**+**b**=**c**and*a*+*b*=*c*does this mean the the vectors are neither parallel nor perpindicular? (b) If**a**+**b**=**a**-**b**does this mean that**b = 0**? (c)**a**+**b**=**c**and [itex] a^{2} + b^{2} = c^{2} [/itex] this means that**a**and**b**are perpindicular?Any help is appreciated

Thanks

Last edited: