For the vectors u=(2,-3) and w=(-1,2), calculate |-3u| - |2w|.
if u=(2,-3) then -3u = (-6,9)
and │-3u│ = √(36+81) = √117 = 2√13
and │u│ = √(4+9) = √13
what do you observe?
can you finish it?
"and │-3u│ = √(36+81) = √117 = 2√13
"
should have said
and │-3u│ = √(36+81) = √117 = 2√13
Argghhhh!
3√13
To calculate |-3u| - |2w|, we first need to find the magnitude of -3u and the magnitude of 2w.
To find the magnitude of a vector, we use the formula:
|u| = sqrt(u1^2 + u2^2)
For the vector u = (2, -3), we substitute the values into the formula:
|u| = sqrt((2)^2 + (-3)^2)
= sqrt(4 + 9)
= sqrt(13)
Therefore, |u| = sqrt(13).
Similarly, for the vector w = (-1, 2), we substitute the values into the formula:
|w| = sqrt((-1)^2 + (2)^2)
= sqrt(1 + 4)
= sqrt(5)
Therefore, |w| = sqrt(5).
Now we can calculate the expression |-3u| - |2w|:
|-3u| = |-3| * |u|
= 3 * |u|
= 3 * sqrt(13)
|2w| = |2| * |w|
= 2 * |w|
= 2 * sqrt(5)
Finally, we substitute the calculated values into the expression:
|-3u| - |2w| = 3 * sqrt(13) - 2 * sqrt(5)
So, |-3u| - |2w| is equal to 3 * sqrt(13) - 2 * sqrt(5).