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Find the coordinates of the vertices $A,B$, and $C$ of the rectangular box shown to the right. $A=()$ (Simplify your answers.)
Sketch the plane parallel to the $xy$-plane through $(6,7,9)$ and find its equation. Sketch the plane parallel to the $xy$-plane through $(6,7,9)$. Choose the correct graph below. A. B. C.
Find an equation or inequality that describes the following object. A sphere with center $(1,1,4)$ and radius $7 $ The equation or inequality that describes the object is
Find an equation or inequality that describes the following object. A ball with center $(8,4,−1)$ and radius 6 . Choose the correct answer below. A. $(x−8)_{2}+(y−4)_{2}+(z+1)_{2}≤36$ B. $(x+8)_{2}+(y+4)_{2}+(z−1)_{2}≤36$ C. $(x−8)_{2}+(y−4)_{2}+(z+1)_{2}=36$ D. $(x+8)_{2}+(y+4)_{2}+(z−1)_{2}≥36$
Give a geometric description of the following set of points. $x_{2}+y_{2}+z_{2}−6x−18y−8z≤73$ Choose the correct answer below. A. A ball with center $(3,9,4)$ and radius 179 B. A ball with center $(3,9,4)$ and radius $179 $ C. A ball with center $(−3,−9,−4)$ and radius $179 $ D. A ball with center $(−3,−9,−4)$ and radius 179 E. The entire xyz-coordinate system F. The empty xyz-coordinate system
For the vectors $u=⟨3,2,0⟩$ and $v=⟨3,1,2⟩$, evaluate the following expressions. a. $2u+3v$ b. $3u−v$ c. $∣u+3v∣$ a. $2u+3v=⟨,,$
Consider the points $P(4,5,3)$ and $Q(10,13,11)$. a. Find $PQ $ and state your answer in two forms: $⟨a,b,c⟩$ and $ai+bj+ck$. b. Find the magnitude of $PQ $. c. Find two unit vectors parallel to $PQ $. a. Find $PQ $. $PQ =⟨,l=()i+()j+()k$
Find two vectors parallel to $v$ of the given length. $v=PQ $ with $P(4,9,5)$ and $Q(3,5,8)$; length $=52$ The vector in the direction of $v$ is $⟨$, , . (Type exact answers, using radicals as needed.)

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The point is vertically units above the point .

Since the upwards direction is positive ,...