已知三个向量a=(3,-2),b=(-5,1),c=(0,4),求下列各式的值(1)3a^2-4ab+5b^2-6bc-2c^2.

题目

已知三个向量a=(3,-2),b=(-5,1),c=(0,4),求下列各式的值(1)3a^2-4ab+5b^2-6bc-2c^2.
(2)2(ab)c-3(b^2)a+(ac)b

答案

(1)3a^2-4ab+5b^2-6bc-2c^2.
=3*(9+4)-4*(-15-2)+5*(25+1)-6*4-2*16
=39+68+130-24-32
=237-56
=181
(2)2(ab)c-3(b^2)a+(ac)b
=2*(-15-2)(0,4)-3(25+1)(3,-2)+(-8)(-5,1)
=(-34)(0,4)-78(3,-2)+(-8)(-5,1)
=(-228,12)