If vector u = 20 m �due North and vector v =10 m � at 30 degrees East of North, find u + v and u − v.

Answer 1

u = (20cos90, 20sin90) = (0 , 20)
v = (10cos60, 10sin60) = (5 , 5√3)

u+v = (5 , 20 + 5√3)
u - v = (-5 , 20 - 5√3)

check by making a vector diagram sketch

Answer 2

calculations

Answer 3

if vector u =20m due north and vector v =10m at 30 degrees E of N,find u + v and u - v.

Answer 4

I don't know 😕 🤷 😐 😔
Can you show me the steps

Answer 5

U+v=30
u_v=10

Answer 6

To find the sum of vectors `u` and `v`, we can add their components separately.

Let's start by finding the components of vector `v`:

- The x-component of `v` is `10 cos(30°) = 8.66 m`.
- The y-component of `v` is `10 sin(30°) = 5 m`.

Now let's add the components of `u` and `v`:

- The x-component of `u + v` is `0 + 8.66 = 8.66 m`.
- The y-component of `u + v` is `20 + 5 = 25 m`.

Therefore, the sum of vectors `u` and `v` is `u + v = (8.66, 25) m`.

To find the difference of vectors `u` and `v`, we can subtract their components separately.

Let's subtract the components of `v` from `u`:

- The x-component of `u - v` is `0 - 8.66 = -8.66 m`.
- The y-component of `u - v` is `20 - 5 = 15 m`.

Therefore, the difference of vectors `u` and `v` is `u - v = (-8.66, 15) m`.

Answer 7

u+v= 29.1m due to 20°E.
u-v=12.4m due to 23°W

Answer 8

The solution you have provided is not correct.

The correct solution is:

We are given vector `u` = 20 m due North and vector `v` = 10 m at 30 degrees East of North.

To find the sum of `u` and `v`, we can add their components separately.

Let's start by finding the components of vector `v`:

- The x-component of `v` is `10 cos(30°) = 8.66 m`.
- The y-component of `v` is `10 sin(30°) = 5 m`.

Now let's add the components of `u` and `v`:

- The x-component of `u + v` is `0 + 8.66 = 8.66 m`.
- The y-component of `u + v` is `20 + 5 = 25 m`.

Therefore, the sum of vectors `u` and `v` is `u + v = (8.66, 25) m` and it makes an angle of 70 degrees with the positive x-axis.

To find the difference of `u` and `v`, we can subtract their components separately.

Let's start by finding the components of vector `u`:

- The x-component of `u` is `0`.
- The y-component of `u` is `20`.

Now let's subtract the components of `v` from `u`:

- The x-component of `u - v` is `0 - 8.66 = -8.66 m`.
- The y-component of `u - v` is `20 - 5 = 15 m`.

Therefore, the difference of vectors `u` and `v` is `u - v = (-8.66, 15) m` and it makes an angle of 123 degrees with the positive x-axis.

Note: The magnitudes of `u + v` and `u - v` are √(8.66^2 + 25^2) ≈ 27.1 m and √((-8.66)^2 + 15^2) ≈ 17.1 m, respectively.