Question

Determine whether u and v are orthogonal.
u = (-1,3,-1) v = (2,-1,5)

Answer 1

Answer: not orthogonal

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Step-by-step explanation:

We compute the dot product. This is where we multiply corresponding coordinates and add the products.

If

u = (a,b,c)

v = (d,e,f)

then

u dot v = a*d + b*e + c*f

If the result of the dot product is zero, then the vectors are orthogonal.

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So,

u dot v = a*d + b*e + c*f

u dot v = -1*2 + 3*(-1) + (-1)*5

u dot v = -2-3-5

u dot v = -10

The result is nonzero.

It tells us that these vectors are not orthogonal.

The two vectors do not form a 90 degree angle.