How do I find the angle between a line and a plane?

Find the angle between the line r = [3,2,-1] + s[2,6,-5] and the plane 2x +6y -5z -9 = 0. Please explain how you got the answer. And the answer should be 90 degrees.How do I find the angle between a line and a plane?A line is defined by a point, and a directional vector. In this case, the directional vector is %26lt;2,6,-5%26gt;. A plane is defined by a point, and an orthogonal vector. The component form of the orthogonal is given by the coefficients attached to the variables. Since the directional vector that corresponds to the line is the same as the orthogonal vector to the plane, they line is perpendicular to the plane making the angle between them 90 degrees.

As a further note, if you wanted to find the angle between two vectors, you use the formula below.

cos脽=(u鈥)/(||u||*||v||)

This can help you because the plane is orthogonal to the vector that defines it, so you would find the angle between the line and the orthogonal vector, then find the complement of that to get the angle between the line and the plane.