Question #209795

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.


1
Expert's answer
2021-06-23T14:23:19-0400

Solution.

1.1

Find vw=2+2+0=0.v•w=-2+2+0=0.

So vectors vv and ww are orthogonal.

Therefore, vectors vv and ww form a right angle triangle.

1.2


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

Hense

uw=uwcos(<u>,<w>),u•w=||u||•||w||\cos(<u>,<w>),

then


cos(<u>,<w>)=12.\cos{(<u>,<w>)}=\frac{1}{2}.

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



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