To check if two or more vectors are Coplanar.

Question

I have written my own understand for this. Please correct me if I’m right or wrong.

To get two or more vectors to be coplanar , I have noticed that there is a kind of series which forms between the coordinates.

For example : (1,1,1) , (2,2,2) , (3,3,3) .

Similarly , when I made it a little difficult. I still got the same correct result.

If the Q is like : If vector $2i + 2j – 2k$ , $5i + yj + k $and $ -i + 2j + 2k $. Check if the vectors are co planar and then find the value of y?
Then , my approach can be a little too time consuming .

I would like to know if you have any different kind of approach to these kind of questions.

Maybe intuitively or using formula of vectors . Anything.

Thank you.

Answer 1

Hint:

If three vectors are coplanar, cross product of any two is perpendicular to the third one.