Question

In Exercises \(51-56,\) find the vector \(z,\) given that \(\mathbf{u}=\langle 1,2,3\rangle\) \(\mathbf{v}=\langle 2,2,-1\rangle,\) and \(\mathbf{w}=\langle 4,0,-4\rangle\) \(\mathbf{z}=\mathbf{u}-\mathbf{v}\)

Short answer

Therefore, the vector \(z = u - v\) is \(\langle -1, 0, 4 \rangle\).

Step-by-step solution

Subtract corresponding components of vectors

To obtain the vector \(z\) as the result of subtracting vector \(v\) from vector \(u\), simply subtract the components of vector \(v\) from the corresponding components of vector \(u\). This means that the first component of \(z\) is the first component of \(u\) minus the first component of \(v\) (that is, 1 - 2), the second component of \(z\) is the second component of \(u\) minus the second component of \(v\) (that is, 2 - 2), and the third component of \(z\) is the third component of \(u\) minus the third component of \(v\) (that is, 3 - (-1)).

Compute the subtraction

Perform the subtraction for each component. The first component of \(z\) is \(1 - 2 = -1\), the second is \(2 - 2 = 0\), and the third is \(3 - (-1) = 4\).