Question

Given that P = (-5, 5) and Q = (-13, 10), find the component form and magnitude of 2 vector PQ.

Answer 1

<-16, 10>, square root of 178

Explanation:

The other user was close, BUT he forgot to multiply his work by 2, and there were a few miscalculations.

The formula to find PQ respectively is <q1-p1,q2-p2> (Note: if they ask you to find QP then just flip the formula to <p1-q1,p2-q2>)

-13-(-5)=-8

10-5=5

Multiply them by 2 to get <-16,10>

To get the magnitude you use the same formula for the first part before, then you square both of them and add them together, then take the square root.

-13-(-5)=-8

-8^2=64

10-5=5

5^2=25

64+25=89

89*2=178

Take the square root: (square root of 178)

Then your done!

Answer 2

Define unit vectors along the x-axis and the y-axis as
`\hat{i} , \, \hat{j}` respectively.

Then the vector from P to Q is

`\vec{PQ} = (-13+5)\hat{i} + (10-5)\hat{j} = -8\hat{i} + 5\hat{j}`
In component form, the vector PQ is (-8,5).

The magnitude of vector PQ is
√[(-8)² + 5²] = √(89) = 9.434

Answer:
The vector PQ is (-8, 5) and its magnitude is √89 (or 9.434).