Let u = (3, 4) and suppose v = (a, b) is a unit vector orthogonal to u. Then | b| equals:

|b| = 3/5 = 0.6

Step-by-step explanation:

Two vectors

W = (w₁, w₂)

V = (v₁, v₂)

Are orthogonal if their dot product is equal to zero, this is:

W.V = 0 = w₁*v₁ + w₂*v₂

Here we know that:

u = (3, 4) and v = (a, b) are orthogonal.

And v is an unit vector, which means that:

II v II = 1 = √( a^2 + b^2)

or simply:

1 = a^2 + b^2

And because these vectors are orthogonal, we also have that:

3*a + 4*b = 0

Then we have two equations:

1 = a^2 + b^2

3*a + 4*b = 0

We want to find the value of |b|

For that, we can start by isolating a in the second equation, so we get:

3*a = -4*b

a = (-4/3)*b

Now we can replace that in the first equation to get:

1 = ((-4/3)*b)^2 + b^2

1 = (16/9)*b^2 + b^2

1 = (25/9)*b^2

1*(9/25) = b^2

(9/25) = b^2

Then we will have that:

|b| = √b^2 = √(9/25) = 3/5

|b| = 3/5 = 0.6

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24