find an ordered pair to represent vector u in u = (3/4)w-2v if vector w = <-2/3,4> and vector v = <3/8,-2>
How do i do this?
(3/4)w = -1/2 i + 3 j
-2v = -3/4 i + 4 j
add for u
u = -5/4 i + 7 j = < -5/4 , 7> in your notation
@Damon: Thank you!
To find the ordered pair representation of vector u, you can substitute the given values of vectors w and v into the equation u = (3/4)w - 2v.
Given:
Vector w = <-2/3, 4>
Vector v = <3/8, -2>
Substituting the values:
u = (3/4)(-2/3, 4) - 2(3/8, -2)
Simplifying the equation:
u = (-1/2, 3) - (6/8, -4)
To subtract vectors, subtract each corresponding component separately:
u = (-1/2 - 6/8, 3 - (-4))
Calculating:
u = (-4/8 - 6/8, 3 + 4)
Simplifying:
u = (-10/8, 7)
Therefore, the ordered pair representation of vector u is (-10/8, 7).
To find the ordered pair representing vector u, you will need to substitute the values of vectors w and v into the equation u = (3/4)w - 2v.
Let's start by substituting the values of vector w and vector v into the equation:
vector w = <-2/3,4>
vector v = <3/8,-2>
Now, we can substitute these values into the equation:
u = (3/4)(-2/3,4) - 2(3/8,-2)
To simplify this expression, we need to perform the multiplication and subtraction:
u = (-6/12,8/4) - (6/8,-4)
Now, let's simplify each component of the vector:
u = (-1/2, 2) - (3/4, -4)
To subtract the vectors, we need to subtract the corresponding components:
u = (-1/2 - 3/4, 2 - (-4))
Finding a common denominator for the first component:
u = (-2/4-3/4, 2 + 4)
Simplifying the first component:
u = (-5/4, 6)
Therefore, the ordered pair representing vector u is (-5/4, 6).