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T F If two planes ax + by + cz = d and Ax+By+Cz = D are parallel, then a = A, b = B, and c= C.

T F If two planes ax + by + cz = d and Ax+By+Cz = D are parallel, then a = A, b = B, and c= C.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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T T T T T T T T T T T T are needed. F If two planes ax + by + cz = d and Ax+By+Cz = D are parallel, then a = A, b = B, and c = C. F F F Two nonzero vectors u and v are perpendicular if u x v = 0. The curvature of the helix r(t) = (cos(t), sin(t), t) at any t is less than 1. F The curvature of a circle with radius 3 is 1/3. F There are unit vectors v and w in space for which v xw| = 2. F The vector projection of (2, 3, 1) onto (1, 1, 1) is parallel to (1, 1, 1). F If two planes do not intersect, then their normal vectors are parallel. F If u (v xw) = 0, then all three vectors u, v, w are in the same plane. FIf f(x, y) has fy(x, y) = 0, then f must be constant. F If lim f(x, y) exists, then f(x, y) is continuous at (a, b). (x,y) →(a,b) Every point on curve r(t) = (t, t², -t) lies on the surface cz + y = 0. The curvature of the curves r(t) = (t, t², t³) and R(t) = (t², t², t6) are the same at t = 1. F
Transcribed Image Text:T T T T T T T T T T T T are needed. F If two planes ax + by + cz = d and Ax+By+Cz = D are parallel, then a = A, b = B, and c = C. F F F Two nonzero vectors u and v are perpendicular if u x v = 0. The curvature of the helix r(t) = (cos(t), sin(t), t) at any t is less than 1. F The curvature of a circle with radius 3 is 1/3. F There are unit vectors v and w in space for which v xw| = 2. F The vector projection of (2, 3, 1) onto (1, 1, 1) is parallel to (1, 1, 1). F If two planes do not intersect, then their normal vectors are parallel. F If u (v xw) = 0, then all three vectors u, v, w are in the same plane. FIf f(x, y) has fy(x, y) = 0, then f must be constant. F If lim f(x, y) exists, then f(x, y) is continuous at (a, b). (x,y) →(a,b) Every point on curve r(t) = (t, t², -t) lies on the surface cz + y = 0. The curvature of the curves r(t) = (t, t², t³) and R(t) = (t², t², t6) are the same at t = 1. F
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