Answer
Since 0 = 0, the vectors are orthogonal.
Work Step by Step
Note: Vectors can be rewritten using <>, so
u = <12, 3, -5>
v = <2, -3, 3>
A vector is orthogonal if the dot product of the two vectors is 0, so we have to check if uāv = 0.
The dot product can be formed by multiplying the first components of the vector together, multiplying the second components of the vector together, multiplying the third components of the vector together, and adding all the products together.
1. Multiply the first components: 12 * 2 = 24
2. Multiply the second components: 3 * -3 = -9
3. Multiplying the third components: -5 * 3 = -15
3. Add the products together: 24 + (-9) + (-15) = 0
Since 0 = 0, the vectors are orthogonal.