wektory xxx: wyznaczyć wektor d oraz liczbę m ,które można otrzymać z podanych wektorów: a (5 ,− ,5, 10) , b = (1,1,0) c (−6,0 ,12) d= 2a − 5b +c. m = a*b. obliczyć długość wektora d wie ktoś jak to zrobic?

Janek191: → a = [ 5 , − 5 ,10 ] → b = [ 1 , 1 , 0 ] → c = [ − 6 , 0 , 12 ] więc → → → → d = 2 a − 5 b + c = 2*[ 5, − 5, 10 ] − 5 *[ 1 , 1, 0 ] + [ − 6, 0, 12 ] = = [ 10 , − 10 , 20 ] + [ − 5 , − 5 , 0 ] + [ − 6. 0 , 12 ] = = [ 10 + (−5) + ( − 6) , − 10 + (−5) + 0 , 20 + 0 + 12 ] = [ −1 , − 15, 32 ] Długość wektora d = √ ( − 1)² + (−15)² + 32² = √1 + 225 + 1024 = √ 1 250 = = √ 25*25*2 = 25 √2 −−−−−−−−−−−−−−−−− oraz iloczyn skalarny → → m = a * b = [ 5, − 5, 10 ] * [ 1 , 1 , 0 ] = 5*1 + (−5)*1 + 10*0 ] = 5 − 5 + 0 = 0 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Janek191: → a = [ 5 , − 5 ,10 ] → b = [ 1 , 1 , 0 ] → c = [ − 6 , 0 , 12 ] więc → → → → d = 2 a − 5 b + c = 2*[ 5, − 5, 10 ] − 5 *[ 1 , 1, 0 ] + [ − 6, 0, 12 ] = = [ 10 , − 10 , 20 ] + [ − 5 , − 5 , 0 ] + [ − 6. 0 , 12 ] = = [ 10 + (−5) + ( − 6) , − 10 + (−5) + 0 , 20 + 0 + 12 ] = [ −1 , − 15, 32 ] Długość wektora d = √ ( − 1)² + (−15)² + 32² = √1 + 225 + 1024 = √ 1 250 = = √ 25*25*2 = 25 √2 −−−−−−−−−−−−−−−−− oraz iloczyn skalarny → → m = a * b = [ 5, − 5, 10 ] * [ 1 , 1 , 0 ] = 5*1 + (−5)*1 + 10*0 ] = 5 − 5 + 0 = 0 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

xxx: dziękuje