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3. Give the parametric and symmetric equations of the line that passes through the point (2,3,-1) and is perpendicular to both lines L₁ and L₂ z = 1+ t r = 1 L1:y=3t and L2y=-3+3s 2=1-t where s, t€ R.

3. Give the parametric and symmetric equations of the line that passes through the point (2,3,-1) and is perpendicular to both lines L₁ and L₂ z = 1+ t r = 1 L1:y=3t and L2y=-3+3s 2=1-t where s, t€ R.

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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1. B Consider A = 8i - 12j, B = 2i + 14j and C = 18i - 10j. (a) In R² space, draw the vectors A, B, and C in position representation. (b) Find the unit vector having the same direction as 6A + 3B. (c) Find scalars z and y such that zA-yB=-C. 2. Let A = (1,-1,0) and B=(2, 1,-2). (a) Solve for projgA. (b) Find the angle between projgA and A. 3. Give the parametric and symmetric equations of the line that passes through the point (2,3,-1) and is perpendicular to both lines L₁ and L₂ z = 1+t z=1 L1:y=3t and L2 y = −3+3s z=1-t 2=8 where s, t E R. 4. The plane contain the points P(1,-1,-4) and Q(2, 1,-3). Moreover, it contains the line I y +3= 2 3 Determine the general equation of the plane 2. Also, sketch the graph of . 5. IDENTIFY and SKETCH the graph of the following equations in R³. Make sure to rewrite the equations in standard form. (a) x² + y² + 2²-2r-2ky-z+k²+ = 0, where k>0 (b) 2:³0. Show the trace you use. = (c) 9x² + y² + 3622-18-72z+28= 0. Show the traces as well.
Transcribed Image Text:1. B Consider A = 8i - 12j, B = 2i + 14j and C = 18i - 10j. (a) In R² space, draw the vectors A, B, and C in position representation. (b) Find the unit vector having the same direction as 6A + 3B. (c) Find scalars z and y such that zA-yB=-C. 2. Let A = (1,-1,0) and B=(2, 1,-2). (a) Solve for projgA. (b) Find the angle between projgA and A. 3. Give the parametric and symmetric equations of the line that passes through the point (2,3,-1) and is perpendicular to both lines L₁ and L₂ z = 1+t z=1 L1:y=3t and L2 y = −3+3s z=1-t 2=8 where s, t E R. 4. The plane contain the points P(1,-1,-4) and Q(2, 1,-3). Moreover, it contains the line I y +3= 2 3 Determine the general equation of the plane 2. Also, sketch the graph of . 5. IDENTIFY and SKETCH the graph of the following equations in R³. Make sure to rewrite the equations in standard form. (a) x² + y² + 2²-2r-2ky-z+k²+ = 0, where k>0 (b) 2:³0. Show the trace you use. = (c) 9x² + y² + 3622-18-72z+28= 0. Show the traces as well.
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