Please answer and write correctly and neatly.Given the vector field Ā= 2x2y ax – 2(z-x) ay + 3xyz az:d. The y-coordinate of Q (-3,y,5) if |AQ|=100 and y>0e. The distance between P and Q. c) GivenÃ = 2x²y axA|A| = 100= 1A1²2=-2=> ) A| = (2x²y)² + ( 2 (z-x))² + (3xyz) ²4x² y² + 4 (z-7)²2² + 9x2² y² z²2 (Z-x) ay + 3xyząz→ Theequation of surface is24x4 y² + 4(2-x)² +9x²y²z² = 100002 Step 2GivenA == 2x^2y ax - 2 (Z-x) ay +zxyz azNow Aat P(2₁-3, 4), x=2, y=-3, Z=4Ap = 2(2)2-(-3) a₂-2 (4-2)ay +3 (2)X(-3)(4) az介Ap==Step 36) The unit vector in the directionA at pisA=-24ax - 4ay-729z^A =AP(A)=> A = -24ax-4ay-72az-24ax-4ay-72az√577619an-√√(-2y)²+(-4)²+(-72)²-ay-19189219

Given That : Vector field A→=2x2yax-2(z-x)ay +3xyzaz Point P=(2,-3,4) To Find : d) y coordinate of…

Answered: Please answer and write correctly and…

Please answer and write correctly and neatly. Given the vector field Ā= 2x2y ax – 2(z-x) ay + 3xyz az: d. The y-coordinate of Q (-3,y,5) if |AQ|=100 and y>0 e. The distance between P and Q.

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

Please answer and write correctly and neatly.

Given the vector field Ā= 2x²y a_x– 2(z-x) a_y + 3xyz a_z:

d. The y-coordinate of Q (-3,y,5) if |AQ|=100 and y>0
e. The distance between P and Q.

c) Given
Ã = 2x²y ax
A
|A| = 100
= 1A1²
2
=
-
2
=> ) A| = (2x²y)² + ( 2 (z-x))² + (3xyz) ²
4x² y² + 4 (z-7)²2² + 9x2² y² z²
2 (Z-x) ay + 3xyząz
→ The
equation of surface is
2
4x4 y² + 4(2-x)² +9x²y²z² = 10000
2

Step 2
Given
A =
= 2x^2y ax - 2 (Z-x) ay +zxyz az
Now Aat P(2₁-3, 4), x=2, y=-3, Z=4
Ap = 2(2)2-(-3) a₂-2 (4-2)ay +3 (2)X(-3)(4) az
介
Ap=
=
Step 3
6) The unit vector in the direction
A at pis
A
=
-24ax - 4ay-729z
^
A =
AP
(A)
=> A = -24ax-4ay-72az
-24ax-4ay-72az
√5776
19
an
-
√√(-2y)²+(-4)²+(-72)²
-ay-
19
1892
19

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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