Is this correct?
1. Write v as the sum of 2 vector components if v = 2i + j and w = 3i - 2j
v = (12/13i - 8/13j) + (14/13i + 21/13j)
To determine whether the expression you provided is correct, let's calculate the sum of the vector components.
Given:
v = 2i + j
w = 3i - 2j
To write v as the sum of two vector components, we need to find two vectors, v1 and v2, such that v = v1 + v2.
To find v1 and v2, we can match the coefficients of the i and j terms separately.
For the i component:
v1i + v2i = 2i
Equating the i coefficient on both sides, we get:
v1 + v2 = 2
For the j component:
v1j + v2j = j
Equating the j coefficient on both sides, we get:
v1 - v2 = 1
Solving the system of equations formed by v1 + v2 = 2 and v1 - v2 = 1, we find that v1 = 3/2 and v2 = 1/2.
Therefore, we can write v as the sum of two vector components:
v = (3/2)i + (1/2)j + (1/2)i - (1/2)j
Simplifying, we have:
v = (3/2 + 1/2)i + (1/2 - 1/2)j
v = (2i) + (0j)
v = 2i
Hence, the expression v = 2i is the correct representation of vector v as the sum of two vector components. The expression you provided earlier, v = (12/13)i - (8/13)j + (14/13)i + (21/13)j, does not correspond to the given vectors v and w.