How do you find the unit vector in the direction of the given vector in w = 7i − 3j. can someone explain it for me, i really don't know!
what is the magnitude of that vector?
sqrt (49 + 9) = sqrt 58
so
(1/sqrt 58) (7i - 3 j)
= (7/sqrt 58) i - (3/sqrt 58) j
the magnitude of that vector will be one
49/58 + 9/58 :)
thanks damon
To find the unit vector in the direction of a given vector, you need to follow these steps:
1. Calculate the magnitude (or length) of the given vector.
- In this case, the given vector is w = 7i - 3j.
- To find the magnitude, you can use the formula: |w| = sqrt((x^2) + (y^2)), where x and y are the components of the vector.
- Substituting the values, |w| = sqrt((7^2) + (-3^2)) = sqrt(49 + 9) = sqrt(58).
2. Divide each component of the vector by its magnitude to obtain the unit vector.
- The unit vector in the direction of w can be denoted as u.
- u = (w / |w|) = (7i - 3j) / sqrt(58).
Therefore, the unit vector in the direction of w = 7i - 3j is u = (7i - 3j) / sqrt(58).