Convert these equations to Cartesian coordinates: a) {- Si=r(1– r²)(9 – p²), ló = 1. : = r(1- r²)(4 – r²), (ô = 2 – r².

Q: Find parametric equations for the line through (-2,0,4) parallel to V=2i +4j -2k .

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Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR is…

Q: The formula for vector projection is incorrect, rendering this solution useless. In the formula, it…

A: Let us consider two vector A and B then the angle between two vectors is obtained as cosθ=A·BAB The…

Q: Determine the are of a triangle formed by the given 7x+8y=69 and the coordinate axes x and y.

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Q: A parabolic antenna follows the equation y^2 + 4x = 0. Which of the following is the coordinates of…

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Q: Convert the following point from cylindrical to rectangular coordinates: 11T ,4.5 6 10,

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Q: 2 1- -3 -2 -1 B. -1 -2 The midpoint of AB = ([ ? ], [ ]) %3D Enter 3. 2. A.

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Q: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

Q: Find parametric equations of the line through (-3,0, 3) that is parallel to 5i– 7j+k.

A: Recall:  The parametric equations of the line through (x0,y0,z0) that is parallel to a i+b j+c k is…

Q: An air ambulance is travelling from Barrie to Toronto. Toronto is located 90 km [S5°E] of Barrie. If…

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Q: Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

A: Given  The vector equation is  0i +2j+k  The line passing through origin , origin is  ( 0 ,0 ,0)…

Q: With respect to right-handed Cartesian coordinates, let a = [2, 1, 0], b = [-3, 2, 0], c = [1, 4,…

A: Given: The vectors are a=2,1,0, b=-3,2,0, c=1,4,-2 and d=5,-1,3. To find: The value of the following…

Q: Q1, Find Parame tric equations for the line through the Point (0,1, 2) that is U =i +2} + 3k and ū=…

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

Q: Find the parametric equations for the line in which the planes -4x +y+3= = 5 and 2x+y+ = 3…

A: Given that:-4x+y+3z=5    .............(1)2x+y+z=3          ..............(2)

Q: Write the equations for converting from cylindrical torectangular coordinates. In what situation…

A: Part (a) When to use: If you have a problem with cylindrical symmetry Example: the magnetic field…

Q: Find a parametric description of the line segment with endpoints P(-1,3) to Q(3,-2)

A: The line segments with endpoints P(-1,3) to Q(3,-2)

Q: Write a vector equation for the line segment from P to Q. 4

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Q: Find parametric equations for the line through (-2, 0, 4) parallel to v = 2i + 4j - 2k

A: we know that parametric equation of line which passes through point x0,y0,z0 and parallel to vector…

Q: To which coordinate plane is the plane y = 1 parallel?

A: y=1

Q: Find a parmetric equation that describes the entire set of points (x,y) such that 4x2-9y2=36

A: The given curve can be represented in a different manner as shown on the whiteboard.

Q: If i = v-1, which point shows the location of 5- 2i on the plane?

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Q: Explain how you would convert from a plane's scalar equation to a vecto

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Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: Given 7, -2

Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: Given that the point (5, 0) a) symmetric with respect to the x axis Substitute the coordinate -y for…

Q: Complete the parametric equations for the line where the planes - 7x + y + 3z = 3 and 4x7y + z = 23…

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Q: Calculate the cosine of the angle which the vector 2i+2j-k makes with the positive x-axis

A: Given: find the cosine of the angle which the vector 2i+2j-k makes with positive x axis

Q: Eliminate the parameter 1 to find a Cartesian equation for: x = t² and y = 4 + 2t. and express your…

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Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: (a) Consider the point (-3, 1). Recall that to find the point that is symmetric about the x-axis, we…

Q: Identify the quadric x + y – 22² + 4ry – 2xz + 2yz = 0 and give the equation in standard orm.

A: Write in quadratic form.

Q: sin(r² + y²) dydrdz by converting to a more appropriate coordinate system and then evaluating.

A: Given region of integration is R=x,y,z:-1≤x≤1,-1-x2≤y≤1-x2,0≤z≤1 By changing the cartesian…

Q: Ã = ë, + 3ểy – 2ể, : Calculate the angle between the B = 4ëx – ëy : vectors A* and B". = -3e, - 5ẽ,

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Q: Express the equation in rectençular coordinates

A: The given polar equation is r=asinθ. We have to write the given equation in the rectangular form.

Q: Find the rectangular coordinates for the point given in poloar coordinates:- 4, I a) O(0, 0) b) O…

A: As we know that the polar coordinates are:   x=rcosθy=rsinθ   Given;   -4,π2⇒r,θ

Q: Eliminate the parameter t to find a Cartesian equation for: x = ? and y = 9 + 4t . and express your…

A: We are given that x=t2 and y=9+4t. Now,…

Q: Two planes leave an airport at the same time. One plane is flying at 650 mph at a bearing of N37E,…

A: Let the plane 1 leaves the airport with speed of 650mph at a bearing N 37°E and plane 2 leaves the…

Q: Eliminate the parameter t to find a Cartesian equation for: x = t^2 and y = 3 + 1t and express the…

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Q: Find parametric equations for the line segment thatgoes from Q(0, 3) to P(-2, 0).

A: Given Q(0,3) and P(-2,0)

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i - 2j - k, v = i - k

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Q: The midpoint of AB is M (0, –4). If the coordinates of A are (-8, –7), what are the coordinates of…

A: To find the coordinate of point B. If the coordinate of point A and midpoint of line AB is given.

Q: What is the equation of the vector in a Cartesian coordinate system that originates from the origin…

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Q: find the xy equation of all three sides of triangle ABC with verticies  A= (1,5)  B= (3, -1)  C=…

A: The given triangle is  now we have to find the equation of lines AB,AC,and BC

Q: Which equation represents the perpendicular bisector of AB whose endpoints are A(3,6) and B(- 5,2)?…

A: NOTE: Refresh your page if you can't see any equations. . given points are the slope of the line…

Q: Find the angle, in degrees, between the 2 planes with equations X-y+3z=1 and 3x+ y-z=D2

A: Take the normal vectors of the planes x-y+3z-1=0 and 3x+y-z-2=0 as N1⇀ and N2⇀ respectively.…

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i - 2j + 4k, v = -i + j - 2k

A: Given: The vectors, u=2i-2j+4k and v=-i+j-2k.

Q: Q2 What are the parametric equations for the line through the point (6,-3,1) that is orthogonal to…

A: We have to find the equation of parametric line

Q: If vector C is added to vector B , the result is -9i -8j . If vector B is subtracted from vector C,…

A: If vector C is added to vector B , the result is -9i-8j C+B=-9i-8j If vector B is subtracted from…

Q: Find parametric equations of the line through (-3,1,1) that is parallel to 2i – 5j+k. -

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Q: Which is traveling faster, a car whose velocity vector is 27i⃗ +32j⃗ , or a car whose velocity…

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Q: Find a parametric representation of the solution set of the linear equation. i. x + y = 2 3 x-y - z…

A: We have to find