Answer:
The dot product of U and V is 4.
The vectors U and V are not orthogonal
Step-by-step explanation:
The dot product of the vectors
[tex]\vec X=(x_1,x_2,x_3)[/tex] and [tex]\vec Y=(y_1,y_2,y_3)[/tex] in [tex]R^3[/tex] is given by:
[tex]\vec X\cdot \vec Y=(x_1y_1+x_2y_2+x_3y_3)[/tex]
The dot product of u = <–8, –8, –9> and v = <–7, –7, 12> is
[tex]\vec U\cdot \vec V=(-8,-8,-9)\cdot (-7,-7,12)\\\vec U\cdot \vec V=-8\times-7+-8\times-7+-9\times12\\\vec U\cdot \vec V=-8\times-7+-8\times-7+-9\times12\\\vec U\cdot \vec V=56+56-108\\\vec U\cdot \vec V=4[/tex]
The dot product of orthogonal vectors is zero
Since [tex]\vec U\cdot \vec V=4\ne0[/tex], the two vectors are not orthogonal.
