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# Find two unit vectors orthogonal to both (9, 6, 1) and (−1, 1, 0)?

### 3 Answers

- roderick_youngLv 71 month ago
To get a vector that is orthogonal to two given vectors, take the cross product of the latter two vectors. If you need a review on how to do a cross product, go here https://www.mathsisfun.com/algebra/vectors-cross-p... and scroll down about halfway for an example.

They want a unit vector, so you'll have to scale the vector to have a length 1. For example, suppose the vector is <1, 2, 3> (this isn't the answer to your question, by the way). The length of the vector is sqrt(1^2 + 2^2 + 3^2) = sqrt(14). So we would scale each component by sqrt(14), to get a vector of <1/sqrt(14), 2/sqrt(14), 3/sqrt(14)>

The vector that you got from a cross product corresponds to the right-hand rule. The other vector that is orthogonal to the given vectors goes in the exact opposite direction, and can be found by simply reversing the signs of the first vector. So in the example, it would be <-1/sqrt(14), -2/sqrt(14), -3/sqrt(14)>

- rotchmLv 71 month ago
Hint: The vector u x v is orthogonal to vectors u & v.

Normalize. Two directions.

Hopefully no one will spoil you the answer. That would be very irresponsible of them. Too late. Don't forget to vote me best answer for being the first to correctly walk you through without expliciting in the answers!

- az_lenderLv 71 month ago
The cross product of <9,6,1> and <-1,1,0> would be

<1,-1,15>. A unit vector in this direction is

[1/sqrt(291)] <1,-1,15>.

A unit vector in the exact opposite direction is

[1/sqrt(291) < -1,1,-15>.