Question

Can someone please help me!! (the question is attached)

Answer 1

There are at least two ways to go about it.

We can forget we nkow much about vectors and simply enforce the results of the Dot Product or Inner Product.

If (a b c) is the vectoe we seek, then:

<(a b c)(-2 1 0)> = -2a + b = 0
<(a b c)(1 -1 1)> = a - b + c = 0

Solving for a, b, and c, wee see an overdefined system that results in a = c and b = 2c.

Picking a nontrivial example, we get (1 2 1). I'll leave it to you to make it a UNIT vector.

If we really wanted to do it up right, we could remember that we know what a Cross Product is and how to find it. I'll let you demonstrate that.