Given the vectors u = <−3, 7> and v = <5,1>, find 3u + 2v.
first do x components
3(-3) + 2(5) = -9 + 10 = 1
now y components
3(7) + 2(1) = 21 + 2 = 23
< 1, 23 >
To find 3u + 2v, we need to distribute the scalars (3 and 2) to the corresponding components of the vectors u and v, and then add the resulting vectors.
Let's start by multiplying the scalar 3 to vector u:
3u = 3 * <−3, 7> = <3 * −3, 3 * 7> = <-9, 21>
Next, let's multiply the scalar 2 to vector v:
2v = 2 * <5, 1> = <2 * 5, 2 * 1> = <10, 2>
Now, we add the resulting vectors:
3u + 2v = <-9, 21> + <10, 2> = <-9 + 10, 21 + 2> = <1, 23>
Therefore, 3u + 2v = <1, 23>.
To find 3u + 2v, we need to multiply each vector by its corresponding scalar and then add the results.
First, we will find 3u. To do this, we multiply each component of vector u by 3:
3u = 3 * <−3, 7> = <3 * (−3), 3 * 7> = <-9, 21>
Next, we will find 2v. To do this, we multiply each component of vector v by 2:
2v = 2 * <5, 1> = <2 * 5, 2 * 1> = <10, 2>
Now, we can find 3u + 2v by adding the components of the two vectors:
3u + 2v = <-9, 21> + <10, 2> = <-9 + 10, 21 + 2> = <1, 23>
Therefore, 3u + 2v is equal to <1, 23>.