Question

What is {(i.i) + (-i.j) + (-k.k) + (k.i)}.(Ai +Bj + Cz)?

(a) 1

(b) 0

(c) A + B + C

(d) -1

This question was posed to me in an international level competition.

I'm obligated to ask this question of Dot Product and Cross Product topic in division Force Vectors of Engineering Mechanics

Answer 1

Right option is (b) 0

The explanation: {(i.i) + (-i.j) + (-k.k) + (k.i)} = 0. As (1 + 0 + 0 – 1). Cross product of the same plane vectors always give zero. And dot product of the same plane vector gives a scalar quantity.