Violet now comments that there are scalars a and B such that di DE = a EF × EG = B GF x GD State the values of a and B. a = Number B= Number Explain in the essav box below how a and B can be found without explicitly calculating the cross products

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

part d please

Violet chooses four points D, E, F, G in R³, and decides to tell Luna some of the coordinates. However, Violet decides to withhold two of the coordinate
values, and labels them x and z instead. Violet shows Luna the following list:
D= (3,1,0),
E3 (2,5, г).
F = (x, 6, –3),
G = (4,0,1).
Violet also says to Luna, "The points D, E, F, G are the vertices of a parallelogram, though I won't tell you the order of its vertex labelling."
(a)
Help Luna find x and z.
Number
Number
(b)
Find the distance di from the point F to the line through D and E and enter its exact value in the box below:
di
Transcribed Image Text:Violet chooses four points D, E, F, G in R³, and decides to tell Luna some of the coordinates. However, Violet decides to withhold two of the coordinate values, and labels them x and z instead. Violet shows Luna the following list: D= (3,1,0), E3 (2,5, г). F = (x, 6, –3), G = (4,0,1). Violet also says to Luna, "The points D, E, F, G are the vertices of a parallelogram, though I won't tell you the order of its vertex labelling." (a) Help Luna find x and z. Number Number (b) Find the distance di from the point F to the line through D and E and enter its exact value in the box below: di
(d)
Violet now comments that there are scalars a and B such that
di DE = a |EF × EG
= B GF × GD
State the values of a and B.
a =
Number
Number
Explain, in the essay box below, how a and B can be found without explicitly calculating the cross products.
Transcribed Image Text:(d) Violet now comments that there are scalars a and B such that di DE = a |EF × EG = B GF × GD State the values of a and B. a = Number Number Explain, in the essay box below, how a and B can be found without explicitly calculating the cross products.
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