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:

`barv_1*barv_2=0`

`barv_1*barv_2=lt4,5,3gt*lt-2k,2,kgt`

`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.**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now