Answer to Question #209795 in Linear Algebra for Faith

Question

1.let u=<0,1,1>,v=<2,2,0> and w=<-1,1,0> be three vectors in standard form.

1.1.determine which two vectors form a right angle triangle?

1.2.find @:u w, the angel between the given two vectors.

Answer 1

Solution.

1.1

Find $v•w=-2+2+0=0.$

So vectors $v$ and $w$ are orthogonal.

Therefore, vectors $v$ and $w$ form a right angle triangle.

1.2

$$u•w=1$$ $$||u||=\sqrt{2}, ||w||=\sqrt{2}.$$

Hense

$$u•w=||u||•||w||\cos(<u>,<w>),$$

then

$$\cos{(<u>,<w>)}=\frac{1}{2}.$$

From here, the angle between the given two vectors is equal to 60°.