Question

Determine a vector equation for the line that is perpendicular to the vectors 𝑢 = (2,0,1) and 𝑣 = (0,3, −1) and passes through the point (5,2,1).

Answer 1

You want a vector <a,b,c> which is perpendicular to the two given vectors, that is,
you want the cross-product of the two given vectors.
once you have that , the vector equation would be
r = (5,2,1) + t(a,b,c)

I assume you know how to find the cross-product

let me know what you get

Answer 2

I got (-3, 2, 6) as my cross product.
So the final answer would be r = (5,2,1) + t(-3,2,6).
Thank you so much for your help!

Answer 3

correct