- #1
Sandro Romualdez
- 7
- 12
Homework Statement
Given that vector a = (1, 2, -5), b = (-12, 41, 75) and c = a + 2b, explain why (without doing any calculations whatsoever) the value of a•(b x c) = 0
Homework Equations
No specific equations, as the question asks for the value without making any calculations. This problem mostly takes a knowledge of the properties of vectors, vector addition, the dot product, and the cross product.
The Attempt at a Solution
Using calculations, I could probably manipulate the equation and calculate the values/magnitudes of the vectors and stuff, but since the problem asks for a solution without calculations, it would be pretty futile to try..
I know that for the dot product between two vectors to equal zero, the vectors must be perpendicular. The cross product is the vector that is perpendicular to both vectors b and c, but in this case (3D/Three space/R3), aren't there an infinite number of vectors that can be perpendicular to b and c? In that case how would I be able to explain why a•(b x c) is equal to zero?