Answer:
|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
