Find a unit vector in the direction of the given vector.
w = 7i − 3j
my answer is 7.62. is it correct?
yes
no, 7.62 is not a vector.
It is the length of w.
divide w/|w| to get the unit vector.
google will show many examples.
is the answer for unit vector is 0.131
To find a unit vector in the direction of a given vector, you need to divide the vector by its magnitude.
In this case, the given vector is w = 7i - 3j. To find the magnitude of w, you can use the formula:
|w| = sqrt((7^2) + (-3^2))
|w| = sqrt(49 + 9)
|w| = sqrt(58)
So, the magnitude of w is sqrt(58).
To find the unit vector in the direction of w, you need to divide w by its magnitude:
u = w / |w|
u = (7i - 3j) / sqrt(58)
Simplifying further, you get:
u = (7 / sqrt(58))i - (3 / sqrt(58))j
u ≈ 0.9053i - 0.3827j
Therefore, the correct answer for the unit vector in the direction of w is u ≈ 0.9053i - 0.3827j. It does not equal 7.62.