1.1.20 Vector Algebra

\ (\ underline {\ text {condition:}} \) the coordinates of the peaks of the pyramid \ (a b c d \) are given. Required: 1) Write the vectors \ (\ overrightarrow {a b}, \ overrightarrow {a c}, \ overrightarrow {a d} \) in the orthonomated basis \ (\ vec {\ iMath}. \ vec {\ jmath}, \ vec {k} \) 2) find the modules of these vectors; 3) calculate the scalar product \ ((\ overrightarrow {a b}+\ overrightarrow {a c}) \ cdot \ overrightarrow {a d} \); 4) Calculate the vector work \ ((\ overrightarrow {a b}-\ overrightarrow {a c}) \ Times \ Overrightarrow {a d} \). \ (A (3; 3; -3), b (7; 7; -5), C (5; 14; -13), \ quad D (3; 5; -2) \).