The vectors u, v are given by u = 3i + 5j, v = i - 2j. Find scalars a, b such that a(u + v) = 8i + (b - 2)j
Hello where is the answer
To find the scalars a and b, we can start by expanding a(u + v) and equating it to 8i + (b - 2)j.
First, let's compute the sum u + v:
u + v = (3i + 5j) + (i - 2j)
= 3i + i + 5j - 2j
= 4i + 3j
Now, we can express a(u + v) using the expanded form:
a(u + v) = a(4i + 3j)
= 4ai + 3aj
Now, we can equate this to the given vector 8i + (b - 2)j:
4ai + 3aj = 8i + (b - 2)j
To find a, we can compare the coefficients of i on both sides of the equation:
4a = 8
Dividing both sides by 4, we find:
a = 2
Now, we can substitute a = 2 back into the equation and solve for b:
4(2)i + 3(2)j = 8i + (b - 2)j
8i + 6j = 8i + (b - 2)j
Comparing the coefficients of j on both sides, we have:
6 = b - 2
Adding 2 to both sides of the equation, we find:
b = 8
Therefore, the scalars a and b that satisfy the equation a(u + v) = 8i + (b - 2)j are a = 2 and b = 8.