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5. With each stated property, give an example of the 2-space vector field F(x,y). (a) F...

5. With each stated property, give an example of the 2-space vector field F(x,y). (a) F has a constant direction, but ||F|| increases when moving away from the origin. (b) F is perpendicular to the vector field and ||F||=5 everywhere.

Expert Solution

F(x,y) is a 2 space vector

a) F is constant in direction but ||F|| increases when moving away from origin

Think of F as

-------(1)

where x is variable and a is constant

We can consider a as zero also , hence F has constant direction i.e. +ve x axis direction even for non zero a

As a is constant ||F|| increases as x increases

Field F(X,Y) of (1) satisfies both conditions of constant direction and increasing NORM as we move away from origin

b) For ||F|| to be 5 everywhere there are many possibilities of coefficients of x and y

But for F to be perpendicular let us take

such that

Hence

Now for F to be perpendicular to vector field

We can think x=0

then

This is required result

genius_generous answered 2 years ago

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