# The coordinates of the vertices of the ABCD pyramid are given. Required: 1) write the equation of the edge AD

**The coordinates of the vertices of the ABCD pyramid are given. Required: 1) write the equation of the edge AD; 2) write the equation of the ABC face; 3) find the angle between straight line АD and face АBC; 4) write the equation of a straight line passing through point B parallel to the edge AD. A (3.0.0) B (0.-4.2) C (-1.1.-2) D (0.1.7)**

Edge equation

AD = root 3 ^ 2 + 1 ^ 2 + 7 ^ 2 = = 9 + 1 + 49 = root of 59

Face equation A (x- x0) + B (y- y0) + C (z- z0) = 0

(x-3) ((- 4) • (-2) -1 • 2) – (y-0) ((- 3) • (-2) – (- 4) • 2) + (z-0) ((-3) • 1 – (- 4) • (-4)) = 6x – 14y – 19z-18 = 0

angle between straight line АD and edge АBC

γ = arcsin (0) = 0 degrees

write the equation of a straight line passing through point B parallel to the edge AD

l (x- x0) + m (y- y0) + n (z- z0) = 0

-3 (x – (-1)) + (-4) (y – 1) + 2 (z – (-2)) = 0

The desired plane equation:

-3x – 4y + 2z + 5 = 0