Write a formula for a two-dimensional vector field which has all vectors parallel to the xx-axis and all vectors on a horizontal line having the same magnitude

The formula for a two-dimensional vector field will be:

F = F(x,y) = <u(x,y), v(x,y)> = u i + v j;

Where (i,j) are unit vectors in the coordinate directions

To make all vectors parallel to the x-axis
v(x,y)=0
F(x,y) = <u(x,y),0>

To make all vectors on a horizontal line having the same magnitude.
u(x,y) = u(y)
so
F(x,y) = <u(y),0> = u(y) i

Step-by-step explanation:

Let two- dimensional vector field

We have to find the formula for a two-dimensional vector field which has all vectors parallel to the x-axis and all vectors on a horizontal line having the same magnitude.

When all  vector parallel to x- axis then

v(x,y)=0

Then, the vector field can be written as

When all vectors on a horizontal line having the same magnitude then

u(x,y)=u(y)

Substitute the values

Then, we get

Lets use the distributive property and to this...

Fist 8×53 might be hard so lets break it to (50×8)+(3×8)

⇒400+24

⇒424

And we still have the 125 whcih we have to multiply with 424

Here again we do it the same way but its more packed with steps.

424×125

⇒[(400×100+400×25)+(20×100+20×25)+(4×100+4×25)]

⇒[(40000+10000)+(2000+500)+(400+100)]

⇒[(50000)+(2500)+(500)]

⇒50000+2500+500

⇒50000+3000

⇒53000