Simple Vector Questions (Calc 2)

[jlax31]

Hey, I have a few questions about vectors that I would like a double-check on (much appreciated)


1) Determine the sum of the vectors P = 〈7, 9, −5 〉 and Q = 〈7, 5, 4 〉
I have <14,14,-1> --- not sure the last one is right (can it be a negative?)


2) Determine the components of the vector R = 2 P −5 Q
I have <49,43,10>


3) Determine the magnitude (length) of the vector P
I have sqrt(155)


4) Determine the unit vector in the direction of P
I have < 7sqrt(155)/155, 9sqrt(155)/155, -5sqrt(155)/155 > (not sure these are correct)


5) Determine | P − Q |
I ended up with 2.96


Thanks!

 

[mmm4444bot]

1) Determine the sum of the vectors P = 〈7, 9, −5 〉 and Q = 〈7, 5, 4 〉

I have <14, 14, -1> This is correct

can [a component be] negative?

Of course vector components may be negative! You need a better grasp of how vector numbers differ from scalar numbers.

Scalar numbers have value only; vectors have both value and direction. The negative sign simply denotes the opposite direction (i.e., the unit vector in the z-dimension -- scaled by a factor of 5 -- is pointing down instead of up).

2) Determine the components of the vector R = 2 P −5 Q

I have <49, 43, 10>

My result is different. Please show your work.


Your answers for 3) and 4) look correct.


Please show your work on 5), as well.

Cheers :cool:

 

[mmm4444bot]

the unit vector in the direction of P

< 7sqrt(155)/155, 9sqrt(155)/155, -5sqrt(155)/155 >

not sure these are correct

As a self-check, you could have calculated the magnitude of your answer. That vector must have length 1, in order to be a "unit vector", yes?

 

[jlax31]

Ok for #2 I now have < -21, -7, -30 >

 

[jlax31]

for the last part I did p - q = sqrt((7)^2 + (9)^2 + (-5)^2) - sqrt((7)^2 + (5)^2 + (4)^2) = 2.96

 

[mmm4444bot]

for #2 I now have < -21, -7, -30 >

That matches my result. :cool:

 

[jlax31]

maybe the last part is 9.85? hrm.

 

[mmm4444bot]

for the last part I did

sqrt((7)^2 + (9)^2 + (-5)^2) - sqrt((7)^2 + (5)^2 + (4)^2)

That's for |p| - |q|

|p - q| requires you to subtract vector q from vector p first.

Then calculate the magnitude of the resulting vector.

 

[jlax31]

That's for |p| - |q|

|p - q| requires you to subtract vector q from vector p first.

Then calculate the magnitude of the resulting vector.

So, if first it is P-Q then it is <0,4,-9> then sqrt((0)^2 + (4)^2 + (-9)^2) = 9.85 ?

 

[mmm4444bot]

I should not have changed notation from upper-case to lower-case symbols. That's not good form.

Yes, P-Q first. (You may think of the || symbols as grouping symbols, also. Do the vector math inside first, to get a single vector, then calculate its magnitude.)

Yup, you got it.

|P - Q| = 9.85

 

[jlax31]

got it wrong because i didn't put sqrt(97) T_T ... not fair but i may get the point for it.

 

[mmm4444bot]

got it wrong because i didn't put sqrt(97)

With machine teachers, ya gotta first know the rules of the game. :cool: