Question

If A is the point (1,-1,2),B is the (-1,2,2)and C is the (4,3,0),fine the direction cosines of BA andBC

Answer 1

1) BA

$$\vec{BA}=(1,-1,2)-(-1,2,2)=(2,-3,0)$$

$$\alpha=\frac{2}{\sqrt{2^2+3^2+0^2}}=\frac{2}{\sqrt{13}}\\\beta=\frac{-3}{\sqrt{2^2+3^2+0^2}}=\frac{-3}{\sqrt{13}}\\\gamma=\frac{0}{\sqrt{2^2+3^2+0^2}}=0$$

2) BC

$$\vec{BC}=(4,3,0)-(-1,2,2)=(5,1,-2)$$

$$\alpha=\frac{5}{\sqrt{5^2+1^2+2^2}}=\frac{5}{\sqrt{30}}\\\beta=\frac{1}{\sqrt{5^2+1^2+2^2}}=\frac{1}{\sqrt{30}}\\\gamma=\frac{-2}{\sqrt{5^2+1^2+2^2}}=\frac{-2}{\sqrt{30}}$$