1.1.71 Vector Algebra

Condition: the peaks of the pyramid \ (a b c d: a (2.3.1), b (4.1, -2), c (6.3.7) \), \ (D (7.5, -3) \) 1) to build a pyramid in the CARO COordinates 2) to determine the coordinates and lengths of the vectors \ (\ overline {a b}, \ overline {a c}, \ overLine {a d} \) 3) determine the direction \ (\ overLine {a b} \) (its guide cosines) 4) find \ ((\ overLine {a b}, \ vener {a c}) \) 5) find the projection of the vector \ ( \ overline {a c} \) to the direction \ (\ overLine {a b} \) 6) calculate \ ([\ overLine {a b}, \ overline {a c}] \) 7) calculate \ (\ overline {a b}, \ overLine {a C})^{2} \) 8) Write out the equation of the plane passing through the points \ (a, b, c \) 9) Find the area of the face \ (A b c \) 10) Find the volume of the pyramid \ (A b c d \) 11) Write the equation of the height lowered from the top \ (d \) to the face \ (a b c \) 12) find the length of the height, find the length of the height. lowered from the point \ (d \) to the line \ (a b c \).