Question

i,j,k是三个不共面的向量,向量AB=i-2j+2k,向量BC=2i+j-3k,向量CD=λi+3j-5k,且ABCD

Answer 1

CD = k1AB + k2CDλi+3j-5k = k1(i-2j+2k) + k2(2i+j-3k)=>λ = k1+2k2 (1) and 3 = -2k1+ k2 (2) and-5 = 2k1-3k2 (3)(3) +(2)-2k2=-2k2 =1k1 = -1λ = k1+2k2 = -1+2 = 1