Answer:
[tex]k = \frac{1}{5}[/tex]
Step-by-step explanation:
Two vectors are said to be orthogonal if their dot product is zero.
Dot product:
Suppose we have two vectors, a and b.
a = (1,2)
b = (2,3)
Their dot product is:
a.b = (1,2).(2,3) = 1*2 + 2*3 = 8
In this problem:
u = (2,3)
v = (k + 1, k - 1)
So
u.v = (2,3).(k + 1, k - 1) = 2(k + 1) + 3(k - 1) = 2k + 2 + 3k - 3 = 5k - 1
For the vectors to be orthogonal, the dot product has to be 0. So:
[tex]5k - 1 = 0[/tex]
[tex]5k = 1[/tex]
[tex]k = \frac{1}{5}[/tex]
