Determine the value of k, so that u = [-3,7] and v = [16,k] are perpendicular.
they're parallel
it says determine the value of k so that u and v ARE perpendicular .... if it was parallel, i don't think it would ask me to find k....... unless it's a trick question ...
slope of u = -7/3
so slope of perpendicular to u = +3/7
so
3/7 = k/16
7 k = 48
k = 48/7
or...
their dot product must be zero
(-3)(16) + 7k = 0
7k = 48
k = 48/7
thank you everyone
To find the value of k that makes u and v perpendicular, we need to use the property that the dot product of two perpendicular vectors is zero.
The dot product of two vectors u = [u₁, u₂] and v = [v₁, v₂] is given by the formula:
u · v = u₁ * v₁ + u₂ * v₂
In this case, u = [-3, 7] and v = [16, k]. So we have:
u · v = -3 * 16 + 7 * k
To make u and v perpendicular, we need the dot product to be zero. Therefore:
-3 * 16 + 7 * k = 0
Now, let's solve this equation for k.
-48 + 7 * k = 0
Adding 48 to both sides:
7 * k = 48
Finally, divide both sides by 7:
k = 48 / 7
Therefore, the value of k that makes u and v perpendicular is k = 48/7.