6.3 H 6Find TG) bg using the standowd ma tria and the welativematrix relative to B and 8'.T:R-> R°, TCxy)= ( x +], *,), v=(1,3), 8= {(1, -1), co,)},g'-{c,0), (0,), (1, 0.1}O the stan dand matiaTV) =O the mabix a latine to B and 8' (in terms of thestandand bais)*Tcr)=

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6.3 # 6 Find TG) bq using the standwd ma tria and the matrix ralative to B and 8'. ative MA T:RR°, TC^y) = ( x+J, *,), v=(1,3), 8- {C1,-), co,}, O the stan dand matia T(v) = %3D O the makrix alatine to B and 8' (in terme of the standand baris) * Ter)=

6.3 # 6 Find TG) bq using the standwd ma tria and the matrix ralative to B and 8'. ative MA T:RR°, TC^y) = ( x+J, ,), v=(1,3), 8- {C1,-), co,}, O the stan dand matia T(v) = %3D O the makrix alatine to B and 8' (in terme of the standand baris) Ter)=

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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Question

6.3 H 6
Find TG) bg using the standowd ma tria and the welative
matrix relative to B and 8'.
T:R-> R°, TCxy)= ( x +], *,), v=(1,3), 8= {(1, -1), co,)},
g'-{c,0), (0,), (1, 0.1}
O the stan dand matia
TV) =
O the mabix a latine to B and 8' (in terms of the
standand bais)*
Tcr)=

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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)
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2.3(4) Determines the vector equation of the line of intersection of the plan: (shown in the image)
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)