Question

D= 7i + 9j - 4k

E= 8i + 9j + 5k

Calculate D × E

Find the angle between d and e

Show that D × E is perpendicular to both D and E

Answer 1

$${\bf D}\times {\bf E}=( 7i + 9j - 4k)\times (8i + 9j + 5k)\\ =63k-35j-72k+35i-32j+36i\\ =71i-67j-9k$$

$$\theta=\sin^{-1}\frac{\sqrt{71^2+67^2+9^2}}{\sqrt{6^2+9^2+4^2}\sqrt{8^2+9^2+5^2}}$$

$$\theta=41^\circ$$