Problem number 1.22 only. Thanks! CHAP. 1]VECTOR ANALYSIS111.20. Given the plane 4x + 3y + 2z = 12, find the unit vector normal to the surface in the direction awayfrom the origin.Ans. (4a, + 3n, + 2n,)/V201.21. Find the relationship which the cartesian components of A and B must satisfy if the vector fields areeverywhere parallel.AAns.В, В, В,1.22. Express the unit vector directed toward the origin from an arbitrary point on the line describedby x=0, y=3.-3m, – zm,V9 + zAns.1.23. Express the unit vector directed toward the point (x,, y, z.) from an arbitrary point in theplane y --5.(x, – x)m, + (y, + 5)a, + (z, - z)m,V(x, – x)' + (y, + 5)' + (z, – z)Ans1.24. Expreas the unit vector dirccted toward the point (O,0, h) from an arbitrary point in the plane --2.-Xn, - ya, + (h + 2)m,V + y' + (h + 2)?Ans.Given A-Sn, and B-4a, + B,,, find B, such that the angle between A and B is 45°. If B alsohas a term B,",, what relationship must exist between B, and B,?1.25.Ans. B, - ±4, VB; + B; = 41.26. Show that the absolute value of A•B×C is the volume of the parallelepiped with edges A, B, and C.(Hint: First show that the base has area (BXC].)1.27. Given A-2a, -,, B-3m, +a,, and C=-2a, + 6a, - 4a, show that C is 1 to both A and B.1.28. Given A-, -a,, B= 2n,, and C=-, + 3a,, find A BXC. Examine other variations ofthis scalar triple product.Ans. -4. t41.29. Using the vectors of Problem 1.28 find (AX B) x C.Ans.-8a,1.30. Find the unit vector directed from (2, –5, –2) toward (14, –5, 3).5, +1312Ans.131.31. Find the vector directed from (10, 3x/4, x/6) to (5, x/4, x), where the endpoints are given in sphericalcoordinates.Ans.-9.66m, – 3.54m, + 10.61a,1.32. Find the distance between (2, x/6, 0) and (1, A, 2), where the points are given in cylindricalcoordinates.Ans. 3.531.33. Find the distance between (1, x/4, 0) and (1, 3x/4, x), where the points are given in sphericalcoordinates.Ans. 2.01.34. Use spherical coordinates and integrate to find the area of the region 0spsa on the spherical shellof radius a. What is the result when a= 2x?Ans. 2aa', A = 4ta?1.35. Use cylindrical coordinates to find the area of the curved surface of a right circular cylinder of radius aand height h.Ans. 2nah

Name: Problem number 1.22 only. Thanks! CHAP. 1]VECTOR ANALYSIS111.20. Given
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Description: Problem number 1.22 only. Thanks! CHAP. 1]VECTOR ANALYSIS111.20. Given the plane 4x + 3y + 2z = 12, find the unit vector normal to the surface in the direction awayfrom the origin.Ans. (4a, + 3n, + 2n,)/V201.21. Find the relationship which the cartes

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Problem number 1.22 only. Thanks! CHAP. 1]VECTOR ANALYSIS111.20. Given the plane 4x + 3y + 2z = 12, find the unit vector normal to the surface in the direction awayfrom the origin.Ans. (4a, + 3n, + 2n,)/V201.21. Find the relationship which the cartesian components of A and B must satisfy if the vector fields areeverywhere parallel.AAns.В, В, В,1.22. Express the unit vector directed toward the origin from an arbitrary point on the line describedby x=0, y=3.-3m, – zm,V9 + zAns.1.23. Express the unit vector directed toward the point (x,, y, z.) from an arbitrary point in theplane y --5.(x, – x)m, + (y, + 5)a, + (z, - z)m,V(x, – x)' + (y, + 5)' + (z, – z)Ans1.24. Expreas the unit vector dirccted toward the point (O,0, h) from an arbitrary point in the plane --2.-Xn, - ya, + (h + 2)m,V + y' + (h + 2)?Ans.Given A-Sn, and B-4a, + B,,, find B, such that the angle between A and B is 45°. If B alsohas a term B,&#34;,, what relationship must exist between B, and B,?1.25.Ans. B, - ±4, VB; + B; = 41.26. Show that the absolute value of A•B×C is the volume of the parallelepiped with edges A, B, and C.(Hint: First show that the base has area (BXC].)1.27. Given A-2a, -,, B-3m, +a,, and C=-2a, + 6a, - 4a, show that C is 1 to both A and B.1.28. Given A-, -a,, B= 2n,, and C=-, + 3a,, find A BXC. Examine other variations ofthis scalar triple product.Ans. -4. t41.29. Using the vectors of Problem 1.28 find (AX B) x C.Ans.-8a,1.30. Find the unit vector directed from (2, –5, –2) toward (14, –5, 3).5, +1312Ans.131.31. Find the vector directed from (10, 3x/4, x/6) to (5, x/4, x), where the endpoints are given in sphericalcoordinates.Ans.-9.66m, – 3.54m, + 10.61a,1.32. Find the distance between (2, x/6, 0) and (1, A, 2), where the points are given in cylindricalcoordinates.Ans. 3.531.33. Find the distance between (1, x/4, 0) and (1, 3x/4, x), where the points are given in sphericalcoordinates.Ans. 2.01.34. Use spherical coordinates and integrate to find the area of the region 0spsa on the spherical shellof radius a. What is the result when a= 2x?Ans. 2aa', A = 4ta?1.35. Use cylindrical coordinates to find the area of the curved surface of a right circular cylinder of radius aand height h.Ans. 2nah

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solution : Given the point x=0, y=3 and z1.22unit vector is defined…

Express the unit vector directed toward the origin from an arbitrary point on the line described by x-0, у-3. За, — га, V9 +z Ans.