2. Give that the vectors u=[2, t, -4] and v=[1, -3, t-4] are perpendicular, find the value of the constant, t.
Two vectors u and v are perpendicular if the dot product u.v=0.
Do the multiplication and equate to zero to solve for t.
You want u.v=0
2 - 3t - 4(t-4) = 0
t = 18/7
like that?
Correct!
thanks!
To find the value of the constant, t, you need to use the concept of perpendicular vectors. Two vectors are perpendicular (also known as orthogonal or normal) if their dot product is zero.
Let's calculate the dot product of the given vectors u and v:
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 should be equal to zero:
-7t + 18 = 0
To solve for t, we'll isolate the variable:
-7t = -18
t = -18 / -7
t = 18/7
Therefore, the value of the constant t is 18/7.