Determine a vector of magnitude 2 that is parallel to a=(-3, 4).
To find a vector of magnitude 2 that is parallel to vector a=(-3, 4), we need to scale vector a to have a magnitude of 2.
The magnitude of vector a is given by the formula: |a| = sqrt(a1^2 + a2^2), where a1 and a2 are the components of vector a.
In this case, |a| = sqrt((-3)^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.
To scale vector a to have a magnitude of 2, we divide each component of vector a by its magnitude and then multiply by the desired magnitude.
Let's call the scaled vector b. The components of vector b are given by:
b1 = (a1/|a|) * desired_magnitude = (-3/5) * 2 = -6/5
b2 = (a2/|a|) * desired_magnitude = (4/5) * 2 = 8/5
Therefore, the vector b of magnitude 2 that is parallel to vector a=(-3, 4) is b=(-6/5, 8/5).