Cho hình chóp S.ABCD có 2 mặt phẳng (SAB) và (SAD) cùng vuông góc với (ABCD) . Biết đáy là hình vuông cạnh bằng 2căn2 . Góc giữa đường thẳng SC và (ABCD) bằng 30độ. Khoảng cách giữa đường thẳng BD và S...

To solve this problem, we can use the concept of vectors and trigonometry. First, let's denote the position vectors of points A, B, C, D, and S as $$, $$, $$, $$, and $$ respectively. Given that the base ABCD is a square with side length $$, we have: $$ We are also given that the angle between line SC and plane ABCD is $$. Let's denote the unit vector along SC as $$. Then the projection of BD onto SC is given by: $$ where $$ Now, to find the distance between BD and SC, we can calculate: $$ Substitute $$ into the equation above to get: $$ Simplify this expression to obtain the final answer: $$