Jeśli wektor a = 3i – 4j, a b = -2i + 3k, to ile wynosi suma, różnica, iloczyn skalarny i wektorowy tych wektorów?

[latex]vec a = [ 3;-4; 0] vec b=[-2; 0; 3]\ \ \ vec a + vec b= [ 3;-4; 0]+[-2; 0; 3]=[(3+(-2));((-4)+0);(0+3)]=\ \ =[1;-4; 3]\ \ \ vec a - vec b= [ 3;-4; 0]-[-2; 0; 3]=[(3-(-2));((-4)-0);(0-3)]=\ \ =[5;-4; -3]\ \ \ vec a cdot vec b= [ 3;-4; 0]cdot[-2; 0; 3]=[(3cdot(-2));((-4)cdot0);(0cdot3)]=\ \ =[-6; 0; 0] [/latex] [latex]vec a imes vec b= left[egin{array}{ccc}i&j&k\3&-4&0\-2&0&3end{array} ight] =\ \ \ =ileft[egin{array}{ccc}-4&0\-0&3end{array} ight] -jleft[egin{array}{ccc}3&0\-2&3end{array} ight] +kleft[egin{array}{ccc}3&-4\-2&0end{array} ight] =\ \ \ = i(-4 cdot 3 -0cdot 0)-j(3cdot 3 - 0 cdot (-2) )+k(3 cdot 0 -(-4)cdot (-2) )=\ \ \ =[-12;-9;-8] [/latex]