Question

Please help me out?:) Find u x v and show that it is orthogonal to both u and v. u=6k, v=-i+3j+k . thx

Answer 1

I think the answer is (-18,-6,0) but idk how to prove that it is orthogonal

Answer 2

Well if you're taking the cross product...

Answer 3

take your answers dot product with u and with v. If you get zero, its orthogonal(perpendicular)

Answer 4

Compute the dot product of u X v and u, and then u X v and v. Both of them should be 0.

Answer 5

can you show me?

Answer 6

and is my answer right?

Answer 7

\[(\mathbf{u} \times \mathbf{v})\cdot \mathbf{u}=(-18)(0)+(-6)(0)+(0)(6)=0\\
(\mathbf{u} \times \mathbf{v}) \cdot \mathbf{v}=(-18)(-1)+(-6)(3)+(0)(1)=0\]
Thus, u X v is orthogonal to both u and v.

Answer 8

ok thanks. is my answer correct

Answer 9

yes, your cross product is correct

Answer 10

thx