Question

If vector a = 3i + 4j - 5k and vector b = 7i - 3j + 6k, then find vector((a + b) x (a - b)).

Answer 1

vector a = 3i + 4j - 5k

vector b = 7i - 3j + 6k

vector(a + b) = (3i + 4j - 5k) + (7i - 3j + 6k)

vector(a + b) = 10i + j + k

vector(a - b) = (3i + 4j - 5k) - (7i - 3j + 6k)

= -4i + 7j - 11k

∴ vector((a + b) x (a - b)) = |(i,j,k),(10,1,1),(-4,7,-11)|

= i(-11 - 7) + j(-1 + 0 + 4) + k(70 + 4)

= -18i + 106j + 74k