- #1

Calpalned

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- 6

## Homework Statement

Find the values of

*x*such that the angle between the vectors <2, 1, -1>, and <1, x, 0> is 45 degrees.

## Homework Equations

<2, 1, -1> dot <1, x, 0> = 2 + x

|first vector| = (6)

^{0.5}

|2nd vector| = (1 + x

^{2})

^{1/2}

Angle = cos

^{-1}(a dot b)/(|a||b|)

Cosine of 45 is the root of two divided by two.

## The Attempt at a Solution

I set (2 + x) divided by 6^0.5 and (1 + x

^{2})^0.5 equal to 1 divided by the root of 2.

I eventually get 2√2 + x√2 = √6√1 + x

^{2}

Am I on the right track?