If u= (u1,u2,u3) andv= (v1,v2,v3), then the dot product of u and v is u·v=u1v1+u2v2+u3v3. For instance, the dot product of u=i−2j−3kandv= 2j−kisu·v= 1·0 + (−2)·2 + (−3)(−1) =−1.
Properties of the Dot Product.
Let u,v, and w be three vectors and let c be a real number. Then u·v=v·u,(u+v)·w=u·w+v·w,(cu)·v=c(u·v).
Further, u·u=|u|2.
Thus, if u=0is the zerovector, then u·u= 0, and otherwise u·u>0.1
Orthogonality Two vectors u and v are said to be orthogonal(perpendicular), if the angle between them is 90◦.Theorem. Two vectors u and v are orthogonal if and only if u·v= 0.
Answer:
Correct option: D
Step-by-step explanation:
If we want to shift the graph one unit to the left, we need to add one in the argument of the function, that is, we need to find G(x+1), and we do that by switching the values of x by (x+1) in the equation G(x)
So we have that:
G(x) = x^3 - x^2
Switching all values of x by x+1, we have:
G(x+1) = (x+1)^3 - (x+1)^2
So the correct option is D.
Answer:
dino
Step-by-step explanation:
yup
