Find the value of k for which the plane kx+4y+2z−6=0 is parallel to the line (x−3)/5=y/1=(z)/(−3).

gsragator9

gsragator9

Answered question

2022-09-30

Find the value of k for which the plane k x + 4 y + 2 z 6 = 0 is parallel to the line x 3 5 = y 1 = z 3
So based on this I know the normal to the plane is ( k , 4 , 2 ). I also know the direction vector of the line is ( 5 , 1 , 3 )
I need to find a vector that is perpendicular to the normal, and then somehow use that with the given direction vector to find k, but I'm not quite sure how.

Answer & Explanation

Matteo Estes

Matteo Estes

Beginner2022-10-01Added 9 answers

Hint: Compute the dot product
[ k ; 4 ; 2 ] [ 5 ; 1 ; 3 ]
This product must be zero, then you will get your k

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?