2. Give that the vectors u=[2, t, -4] and v=[1, -3, t-4] are perpendicular, find the value of the constant, t.
You want u.v=0
2 - 3t - 4(t-4) = 0
t = 18/7
thanks Steve!
To determine the value of the constant, t, such that the vectors u and v are perpendicular, we can use the dot product.
The dot product of two vectors u and v is calculated by multiplying their corresponding components and summing the results. For two vectors to be perpendicular, their dot product must be zero.
So, let's calculate the dot product of u and v and set it equal to zero:
u · v = (2)(1) + (t)(-3) + (-4)(t-4) = 2 - 3t - 4t + 16 = -7t + 18
Since the vectors u and v are perpendicular, their dot product u · v must be zero:
-7t + 18 = 0
Now, let's solve this equation for t:
-7t = -18
t = -18 / -7
t ≈ 2.571
Therefore, the value of the constant t that makes the vectors u=[2, t, -4] and v=[1, -3, t-4] perpendicular is approximately t ≈ 2.571.