Finding Reflection of a Vector

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To find the reflection of the vector v = i - 3j + 2k around the line defined by i - k, first calculate the vector projection of v onto the line, denoted as Vp. The reflected vector v' can then be determined using the formula v' = 2Vp - v. Visualizing the vectors with a triangle or parallelogram can aid in understanding the reflection process. This method effectively utilizes vector projection to achieve the desired reflection.
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Find the reflection v' of v=i-3j+2k around the line i-k

how can I do that? I am extremely rusty with math these days;
 
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Call i-k = W. I would calculate the vector projection of V on W, call it Vp. Then the reflected vector is 2Vp-V. Draw a little triangle/parallelogram and you will see it.
 

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