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4. Let u o, where o is the zero vector. Show that there are exactly two unit vectors that is proportional to u.

4. Let u o, where o is the zero vector. Show that there are exactly two unit vectors that is proportional to u.

Advanced Engineering Mathematics
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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\ Let v = (v), v2) be a direction vector on a line e. The mumber 3 2. defined to be the slope of the line ( with, of course, un # 0. Verify the following: (a) Is the definition of 3 well-defined? (b) Show that the line through the point P= (r1, y1) with a slope 3 has the equation y = y1 - B(r - 1). 4. . vectors that is proportional to u. Let u # 0, where o is the zero vector. Show that there are exactly two unit 5. (. that if N' is another unit normal vector to ( and P' is another point on (, then for each X€ E, we have Fix a point P on the line é and let N be normal unit vector to . Show (X – P, N)| = (X – P,N')|
Transcribed Image Text:\ Let v = (v), v2) be a direction vector on a line e. The mumber 3 2. defined to be the slope of the line ( with, of course, un # 0. Verify the following: (a) Is the definition of 3 well-defined? (b) Show that the line through the point P= (r1, y1) with a slope 3 has the equation y = y1 - B(r - 1). 4. . vectors that is proportional to u. Let u # 0, where o is the zero vector. Show that there are exactly two unit 5. (. that if N' is another unit normal vector to ( and P' is another point on (, then for each X€ E, we have Fix a point P on the line é and let N be normal unit vector to . Show (X – P, N)| = (X – P,N')|
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