To find the vector a - b, we need to subtract each component of vector b from the corresponding component of vector a.

Given: $\vec{a} = \langle -5, -1, 5 \rangle$ $\vec{b} = \langle 1, -3, -1 \rangle$

Let's perform the subtraction component-wise:

1. $x$-component: $-5 - 1 = -6$
2. $y$-component: $-1 - (-3) = -1 + 3 = 2$
3. $z$-component: $5 - (-1) = 5 + 1 = 6$

Thus, $\vec{a} - \vec{b} = \langle -6, 2, 6 \rangle$.

So the answer is: $\vec{a} - \vec{b} = \langle -6, 2, 6 \rangle$

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Related Questions

1. How do we find the magnitude of a vector?
2. What is the dot product of two vectors, and how is it calculated?
3. How do we find the cross product of two vectors?
4. How do we determine if two vectors are orthogonal?
5. How do we find the angle between two vectors?

Tip

When performing vector operations, always handle each component separately to avoid calculation errors.