You need to identify the direction vectors to each line, hence, the direction vector of the line given by symmetric equations is `barv_1 = lt4,5,3gt` and the direction vector of the line given by parametric equations is `barv_2=lt-2k,2,kgt.`
The problem provides the information that the lines are orthogonal, hence, the cross product of direction vectors needs to be zero such that:
`lt4,5,3gt*lt-2k,2,kgt = 4*(-2k) + 5*2 + 3*(k)`
`-8k + 10 + 3k = 0 =gt -5k = -10 =gt k = (-10)/(-5)`
`k = 2`
Hence, the lines are orthogonal for k=2, thus the option d) (none of the above) represents the answer.