I am having trouble finding a vector that is perpendicular to both vec(a)=-9 hat(i)+2hat(j)+6hat(k) and vec(b)=-2hat(i)+hat(j)+hat(k) Would it just be 18i+2j+6k?

Cheyanne Jefferson

Cheyanne Jefferson

Answered question

2022-08-12

I am having trouble finding a vector that is perpendicular to both a = 9 i ^ + 2 j ^ + 6 k ^ and b = 2 i ^ + j ^ + k ^
Would it just be 18 i + 2 j + 6 k ?

Answer & Explanation

Alexia Mata

Alexia Mata

Beginner2022-08-13Added 15 answers

Find any solution of
{ 9 x + 2 y + 6 z = 0 , 2 x + y + z = 0.
Set one of the variables arbitrarily and solve for the other two:
x = 4 , y = 3 , z = 5.
sondestiny120g

sondestiny120g

Beginner2022-08-14Added 2 answers

Let a = 9 i ^ + 2 j ^ + 6 k ^ and b = 2 i ^ + j ^ + k ^
Any vector perpendicular to both a and b would be parallel to a × b because a × b always yield a vector perpendicular to both the vectors.
Let the required vector be c , hence
c = λ ( a × b )
c = λ ( 4 i ^ 3 j ^ 5 k ^ ) = 4 λ i ^ 3 λ j ^ 5 λ 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?