Question

Which of the following relations hold true?

(a) i × i = j × j = k × k = 1

(b) i × j = -k, j × i = k

(c) i × i = j × j = k × k = 0

(d) k × i = -j, i × k = j

I got this question in examination.

I'd like to ask this question from Geometrical Applications topic in section Ordinary Differential Equations – First Order & First Degree of Engineering Mathematics

Answer 1

Right answer is (c) i × i = j × j = k × k = 0

The explanation: One of the properties of vector or cross product is, for the orthogonal vectors, i, j, and k, we have the relation,

i × i = j × j = k × k = 0,

i × j = k, j × i = -k,

j × k = i, k × j = -i,

k × i = j, i × k = -j