https://file.aiquickdraw.com/mathbot/file/1730419235226e2yn3n0e.jpg

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:
\[
\vec{a} - \vec{b} = \langle -6, 2, 6 \rangle
\]

Would you like more details or have any questions?

### 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.

Let **a** = <−5, −1, 5> and **b** = <1, −3, −1>. Find **a − b**.

Step-by-step guide to finding the difference between two vectors, a and b, with components a = <−5, −1, 5> and b = <1, −3, −1>. Learn how to perform vector subtraction by calculating the difference for each component. Suitable for high school students in Grades 11-12.

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