7. Let x be the line with equation 2x - 3y = 0 and u:= (a) Find the reflection of u in the line x (b) Find the projection of u on the line x (c) Use (b) to find the distance from u to the line x

Q: The equation of the area of the plane region bounded by y = x^3 and the lines x = 1 and y =0 is…

A: Detail solution written below

Q: 2-) Find the Symmetric form of the equation of the line of in tersection of the two Planes X- +Z =2,…

A:

Q: 2.) Find the Symmetric form of the equation of the line of in tersection of the two Planes X-Y +Z…

A: Let a, b and c be the direction ratios of the required line. Since the required line lies in both…

Q: Let the curve C be the mirror image of the parabola y" the line x+y + 4 = 0 If A and B are the…

A: Given: Parabola:y2=4xLine:x+y+4=0   A and B are the points of intersection of C with the line y=−5…

Q: (b) Compute the slope of the line that is parallel to the xz-plane and tangent to the surface z = x…

A: Given: Let's calculate the slope of the line tangent to the surface z=x(x+y) at the point that is…

Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

A:

Q: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given y'+ye^(3x+7)=-2y² We know that the dy/dx gives the direction field. Hence the given DE can be…

Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

A:

Q: (42) is the distance between the point (1, –3, –2) and the plane x- 4y-3z-2= 0.

A: In this question we have to find the distance between point and plane. Note: As per our policy we…

Q: 1. Determine whether the lines L₁ given by z=t, y=1 with -∞ <t<∞o) and L₂ given by z=2+s, y = 3-2…

A: Introduction: If two lines are parallel then the ratio equality is true between them. And if two…

Q: A circle has a center at the origin and has a radius of R. If x = 10 and y = 20, determine the slope…

A:

Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: Evaluate F- dr where F(, y, z) = (1.5yz cos(ryz), 1.5xzcos(ryz), 1.5xy cos(ryz)) and C (*) is the…

A: We need to evaluate the line integral between the two points.

Q: What is the ALGEBRAIC RULE for REFLECTION over the line y = x? (х, у) —

A: This question is related to reflection of coordinates, We will solve it using given information.

Q: Let L be the line with equation y = x – 1. Find the minimum distance between L and the point (4, 5)…

A: In order to use method of Lagrange multiplier, we first need to find the function to be minimized.…

Q: If the line r = (2-t, -2 + 13t, 8t) is the normal tangent line to the level surface axyz²by² = -14…

A: answer is in next step . please give a like !!

Q: 15. When a line L is tangent to the circle 2 + v = 100 at the point (a, 6), find the equation of…

A:

Q: 2. Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2).

A:

Q: fc z2 dx+ x2 dy +y2 dz, C is the line segment from (1,0,0) to  (4,1,2)

A: Given, r(t)=z2dx+x2dy+y2dz We have the line segment from (1,0,0) to (4,1,2) We parametrize the given…

Q: 4. The tangent of the acute angle between the linesy = 4x – 3 and y = x - 5 is Tano 144() 13 3

A: Please rate

Q: et y = [ 2   3   -1] and u = [ 2   -6   -6] compute the distance d from y to the line through u and…

A: first we shall find equation of line then find distance from line of that point

Q: The distance between the two lines x = 1+ t,y = -2+ 3t, z = 4 – tand x = 2s, y = s, z = s is

A: Please see the explanation below

Q: Find the veeton equation of a Line L going thagh the P= C-6,2) $ paeallel to the ine point %3D…

A:

Q: 4 Find a. the equations of the tangents to the circle x +y + 4x – 2y – 24 = 0 at the points where…

A:

Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

A:

Q: Evaluate S(-x+y+z)dx + (x+y-z)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2,…

A:

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

A:

Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: Suppose there are two lines in the xy-plane in R^2.  These two lines could intersect at a single…

A: let the lines be                              y=m1x+c1y=m2x+c2 given that lines are intersecting in…

Q: Find the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

Q: Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2)

A: Given that: Line is: y=5x+7and collineation is: (x, y)=(2y-x, x-2)

Q: 3- Find the length of the curves in Exercises 1-4. X = (y3/2/3) - y¹/2 from y = 1 to y = 9

A:

Q: | 6. Let y = 3 and u = . Compute the distance from y to the line through u 1 2 and the origin.

A: Given: y=-231  and u=1-12 To compute: the distance from y to the line through u and the origin.…

Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

A:

Q: B. Show that line -- is parallel to plane x-2y+z = 6

A:

Q: Compute (x² + 2y + 3z +1) ds where Cis the line segment from (0, 2, 3) to (2, 5, 7).

A:

Q: Evaluate (x-y+z-2)ds where C is the straight-line segment x=t, y= (1-t), z=1, from (0,1,1) to…

A:

Q: Let ƒ(x, y) = 2x + 3y - 4. Find the slope of the line tangent to this surface at the point (2, -1)…

A:

Q: .11 Compute (1/ry, 1/(x + y)) · dr along the curve (2t, 5t), 1 < t < 4.

A:

Q: Suppose the curve y =x4 +ax3+ bx2+ cx +d has atangent line when x=0  with equation y= 2x +1 and…

A: Given the curve is   y =x4 +ax3+ bx2+ cx +d Differentiating with respect to "x" y' = 4x3 + 3ax2 +…

Q: Suppose a line is given parametrically by the equation L(t)=(1-t, t-4, 1-t) then the vector u and…

A:

Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

A:

Q: Which of the following straight lines are tangent to the curve y = x³ + 4x2 + 7x and passes through…

A: Topic = Geometry  y=7x ia the tangent to the curve.

Q: 17. The tangent of the acute angle between the lines y = 4x – 3 and y = x – 2,is D

A:

Q: 23/ Find the angle between two curves: 3 y = 2 - x² , y = x²

A: The angle between two curves is given by the formula tan θ=f2'x0-f1'x01+f1'x0f2'x0 Given,…

Q: 3. In Eercises, verify that the given point is on the curve and find the lines that are Haltangent…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.