**Question 8**We represent the equation of the ray by:\[ p(t) = (2, 3) + t \cdot (4, 5), \ \text{for } t \in [0, 1] \]What is the initial point of the ray?- ( ) (2, 3)- ( ) (4, 5)- ( ) (2, 2)- ( ) (6, 8)

Answered: Image /qna-images/answer/37ad9de9-d8e2-422b-9190-9da036c813e1.jpg

Answered: QUESTION 8 We represent the equation of…

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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The equation of the plane that passing through the point A(-3, 0, 1) and perpendicular to n= (1, -2, 0) is O x-2y = -3 O x+2y = 3 O x-2z = -3 O x-2z = 3
Question 6 please
Express the given parametric equations of a line using bracket notation and also using i, j, k notation. (a) x = 6t, y = - 4 + 3t O (x, y) = (0, 4) +1 (6,3) ai + bj = -4j + t (6i + 3j) O (x, y) = (0, 4) + t (6, 3) ai + bj = 4j+ t (6i + 3j) O (x, y) = (0, 6) + (-4, 3) ai + bj = − 4j + t (6i + 3j) O(x, y) =(4,0) + t (3,6) ai + bj = −4i + t (3i + 6j) O (x, y) = (6,3)+1(0, - 4) ai + bj (6i + 3j) +t(-4j) (b)x= 4 + 6t,y=4+9t, z = 87t O (x, y, z) = (-4, 4, − 8) +1(-6, ai + bj + ck = 9,7) ( − 4i + 4j - 8 k) + t ( − 6i - 9j + 7k) O (x, y, z) = (4, ai + bj + ck = 4, 8) + t (6, 9, - 7) (4i − 4j + 8 k) + t (6i + 9j – 7k) O (x, y, z) = (6,9, −7) +1(4, - 4,8) ai + bj + ck = (6i + 9j − 7k) + t(4i - 4j + 8k) O (x, y, z) = (-6, 9, 7) + 1 - 4, 4, 8) ai+bj + ck = ( – 6i – 9j + 7k) + t( − 4i + 4j − 8k) O (x, y, z) = (4, 4, 8) + t (6,9,7) ai + bj + ck = (4i +4j + 8 k) + t (6i + 9j + 7k)
I I I I I I I I I I I I - Your answer is partially correct. Find parametric equations of the line through (-3,1 parallel to 4i-8j+ k. www ***** x(t) = 4t-3 y(t) = -8t+ z(t) = t + 6 k 18 X X
The parametric equations 1 (2-1)t x=x₁+ (x2-x1)t, y=y₁+ (Y2 - Y1) where 0 st≤ 1 describe the line segment that joins the points P₁(x, y₁) and P₂(x2, y2). Use a graphing calculator or computer to draw the triangle with vertices A(1, 1), B(4, 3), C(1, 6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t from 0 to 1.) AB BC AC
Express the given parametric equations of a line using bracket notation and also using i, j, k notation. (a) x = 6t, y = - 4 + 3t O (x, y) = (0, - 4) + t (6,3) ai + bj = −4j + t (6i + 3j) O(x, y) = (0, 4) + t (6, 3) ai + bj = 4j + t (6i + 3j) ○ (x, y) = (0, 6) + t ( − 4, 3) ai + bj - 4j + t (6i + 3j) - (x, y) = (-4, 0) + t (3, 6) ai + bj = − 4i + t (3i + 6j) (x, y) = (6, 3) + t(0, − 4) ai + bj = (6i + 3j) + t ( − 4j)
13. Write the parametric equations of the line through the point P(-6, 4, 3), that is perpendicular to both the lines with equations: 4₁ [x, y, z]= [0, -10,- 2]+s[4, 6, -3] L₂ [x, y, z]= [5, 5, -5]++[3, 2, 4]
Which of the following is the parametric equation of the following line with symmetric equation +3 y+2 = 2-1? = 2 Ox=3t-3, y=2t-2, z=2t+1, t € R x=3t+3, y=2t+2, z=2t-1, tER x=3t-3, y=2t-2, z=t+2, ter None of these answers
5. The equation of the circle whose center is the centroid of the triangle with venices (-72 (4,-3) and (6, -5) and passes through (4,2) is ....

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QUESTION 8 We represent the equation of the ray by: p(t) = (2, 3) + t (4, 5), for t in [0, 1]. What is the initial point of the ray? (2, 3) (4,5) (2, 2) O (6,8)