Problem #1: When answering the following true or false questions, please write out the words "TRUE" or "FALSE." (a) The two lines (t) = (2+t, 3-2t, 1-3t) and ₂ (s) = (3+s, -4+3s, 2-7s) intersect at the point (4,-1,-5). The vector (2,3,1) x (3,-4,2) is perpendicular to the plane that contains both lines. (b) (c) (d) point (0,0,-6). multiples. The vector function F(t) = (5 cos(2t), 5 sin(2t), 3) defines a circle. The plane 4x + 3y - 6z = 12 intersects the z-coordinate axis at the If two lines do not intersect, then their direction vectors are scalar
Problem #1: When answering the following true or false questions, please write out the words "TRUE" or "FALSE." (a) The two lines (t) = (2+t, 3-2t, 1-3t) and ₂ (s) = (3+s, -4+3s, 2-7s) intersect at the point (4,-1,-5). The vector (2,3,1) x (3,-4,2) is perpendicular to the plane that contains both lines. (b) (c) (d) point (0,0,-6). multiples. The vector function F(t) = (5 cos(2t), 5 sin(2t), 3) defines a circle. The plane 4x + 3y - 6z = 12 intersects the z-coordinate axis at the If two lines do not intersect, then their direction vectors are scalar
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve first 4 part
Transcribed Image Text:Problem #1: When answering the following true or false questions, please write out the
words "TRUE" or "FALSE."
(a)
The two lines
(t) = (2+t, 3-2t, 1-3t) and ₂ (s) = (3+s, -4+3s, 2-7s)
intersect at the point (4,-1,-5). The vector (2,3,1) x (3,-4,2) is perpendicular to the
plane that contains both lines.
(b)
(c)
(d)
point (0,0,-6).
(e)
If two lines do not intersect, then their direction vectors are scalar
I
The position of a particle is given by F(t) = 4e³ti + 5t². The
acceleration of the particle at t = 0 is 36 î.
multiples.
(f)
Let S be the surface that is part of the cylinder x² + z² = 16 that
lies above the xy-plane and between the planes y = -5 and y = 5. A parametric
representation of S is given by F(u, v) = (4 cos v, u, 4 sin v) where -5 ≤u≤ 5 and 0 ≤
v≤ 2n.
(g)
The vector function (t) = (5 cos(2t), 5 sin(2t), 3) defines a circle.
The plane 4x + 3y - 6z = 12 intersects the z-coordinate axis at the
(h)
Suppose the f(x, y, z) satisfies f(3,7, 1) = 2 and Vf(3,7,1)=
(2,3,8). Then the equation of the tangent plane to the surface f(x, y, z) = 2 at the
point (3,7,1) is 3(x-2)+7(y-3)+1(z - 8) = 2.
The gradient vector field of f(x, y, z)= 8x²y + 2yz³ is given by the
F(x, y, z)= (16x, 8x² + 2z³,6z²)
vector field
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