a,b,c,d为三维列向量A=[a,2c,3d]B=[b,5c,d].且|A|=-12,|B|=15,求|A-B|

题目

a,b,c,d为三维列向量A=[a,2c,3d]B=[b,5c,d].且|A|=-12,|B|=15,求|A-B|

答案

|A-B|
= |a-b, 3c, 2d|
= |a, 3c, 2d| - |b, 3c, 2d|
= 6|a,c,d| - 6|b,c,d|
= |a,2c,3d| - 6/5|b,5c,d|
= |A|-6/5|B|
= -12 -(6/5)*15
= -30.