- #1

lizbeth

- 6

- 0

## Homework Statement

Find the smallest angle between 3x-2y-4z = 5 and {x = 1 + 2t, y = 3 + 4t, z = 5 + 6t}.

## Homework Equations

3x-2y-4z=5 is a plane, the other 3 equations constitute a line.

## The Attempt at a Solution

My understanding is that the angle between a plane and a line can be found by using the direction vector of the line and the normal vector of the plane, and applying the dot product formula,

**n**.

**v**= |

**n**||

**v**|cos Θ.

Doing this, I get that theta is the inverse cosine of -29 / (square root of 29 * square root of 56), which comes out to 130.18 degrees. Since the smallest angle would be the acute angle, I subtracted this from 180 and got 49.82 degrees.

Professor says this is the wrong answer. Can anyone help steer me in the right direction?