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.
The answer would be 82 millimeters!
Answer:
2m if the diameter is 4m
Step-by-step explanation:
Answer: I believe it is h
Step-by-step explanation:
Answer:(4,-2)
Step-by-step explanation: elimination method
3(3x+5y)=2×3
9x+11y=14
9x+15y=6
-
9x+11y=14
4y=-8
y=-2
To get x replace y with -2
3x+(5×-2)=2
3×=12
X=4
