5. Find all vectors such that < 1, 3, 2> x v = < 13, -1, -5 >. 6. Find parametric equations for the line through (2,4,-2) that is perpendicular to plane a+2y+z= 6.

Q: (a) In a Cartesian plane, if the position vector of a moving particle is given by F = ri+ yj, then…

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

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² – 2x + 2y…

A: The given equation is: 2x2+2y2-2x+2y=7...(1)

Q: 8. Find a vector parallel to the line of intersection of the two planes a – 2y + z = 1, 2x + y + z =…

A:

Q: 2. The plane containing the point P(Xg» Yor Zo) and having the normal vector n = (a, b, c) is…

A: Equation of a plane passing through the point Px0, y0, z0 and perpendicular to the vector n=a, b, c…

Q: Find equations for the planes The plane through P0(0, 2, -1) normal to n = 3i - 2j - k

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Q: 1. A plane is defined by the equation x - 7y - 18z = 0. a. What is a normal vector to this plane? b.…

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Q: 2. A plane is defined by the equation 2x - 5y = 0. a. What is a normal vector to this plane? b.…

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Q: Find a vector parametric equation for the ellipse that lies on the plane 5y−3x+z=9 and is inside the…

A: Given that: 5y-3x+z=9 Let x=u cos v, y=u sin v So z=9+3x-5y  =9+3u cos v-5u sin v

Q: 10. Consider the plane P given by r + y – 3z = 0. (a) Find the projection of the vector (2, 1, 0)…

A: Given plane : x+y-3z=0  Projection of A along B is A.B/|B|

Q: Derive a parametric representation and find a normal vector for the plane 6x – 2y + 10z = 16. NOTE:…

A:

Q: 5. Show that lines l and lz intersect, find the point of intersection, then find a parametric…

A: Consider the provided question, Given that,l1: x,y,z=-3,1,5+t2,-2,1l2: x,y,z=13,-6,-2+s4,-1,-3 The…

Q: What is equation of the plane passing through the point A(2, 1,3) and parallel to the vectors a = j-…

A: We have to find the equation of plane passing through point A(2,1,3) and parallel to vectors…

Q: Find parametric equations of the normal line to * + y? at the point (2, 2, 5) the surface z= O r =…

A: In this question we have to find parametric equation of the normal line.

Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

A:

Q: Q The unit vector normal to the plane 2x + 3y+ 6z = 7 is (2ax +3ay +6 az)/7 (2ax - 3ay-6 az)/7 (4ax…

A: The given plane equation is 2x+3y+6z=7. The unit vector normal to the plane ax+by+cz=d is…

Q: Find a vector equation and parametric equations in t for the line through the point and…

A: Given that the point that posses through the line and the line perpendicular to the plane is, P 0 =…

Q: (S'34) 9uq Find vector, parametric, and symmetric equations of the line through (2,3,4) and is…

A:

Q: 6) Consider the plane P : x+y – z = 0 in K³ that contains both the points P1(1,0, 1) and P2(-1,1,0).…

A: Given : plane P : x + y - z = 0  &amp; Points P1(1,0,1) &amp; P2(-1,1,0) To find :  1. Equation of…

Q: The equation of the plane that passes through the point P(1,0,0) and has the vector n = (0,0, 1) as…

A:

Q: 4. A vector normal to the paraboloid z = (x² + y*)/2 is (a) (х, у.1). (b) (2x,2y,–1). (e) (-х,-у.1).

A:

Q: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? A) (2 +…

A: The direction ratio of the normal vector to the plane is (3, 2,1 ) So the perpendicular line to the…

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: Find an equation of the plane that contains the curve with the given vector equation. r(t) = (5…

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Q: Consider the following equation of a plane in R³: -3z – 2y – 3z = -2 Convert your plane to vector…

A: Find the vector parametric form of the plane: -3x - 2y - 3z = -2

Q: 1.20. Given the plane 4x +3y +2z = 12, find the unit vector normal to the surface in the direction…

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Q: Consider the line l in R³ given by the parametric vector equation 3 1 -2 -1 and the plane described…

A: Given that the line l in R3 given by the parametric vector equation and the plane described by the…

Q: 1. a) Given the lines L₁ : 7 = (1,2,−4) + t(k+ 1,3k + 1, k − 3) and L₂: x=2-3s, y = 1-10s, z = 3-5s,…

A:

Q: (2t, 1 – t, 4t) is a parametrization of the line passing through the point (0, 1,0) and also…

A: The statement : &lt;2t, 1-t, 4t&gt; is a parametrization of the line passing through the point (0,…

Q: 1 6. Let L be the line with vector equation +t and let II be the -4 3 plane with equation 3x – 4y +…

A: Given:     Plane with equation π = 3x - 4y + z = 18        Line with vector equation L is…

Q: Find parametric equations for the line through (- 3,1,2) perpendicular to the plane 7x + 9y + 9z =…

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Q: Find the general form of the equation of the plane passing through the point and normal to the…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y?…

A: z = 4x2 + y2  ,  y = ex    We observe that the given two equations, here we can see that y can be be…

Q: The line through the origin parallel to the vector 2j+ k then the parametric equations equals: a) x…

A: Line through origin and parallel to the vector 2j +k is

Q: 9. Find the normal unit vector n to the surface 62 + 2y²+ 2² = 225 at the point P: (5,5, 5).

A:

Q: 1. Assume that the line l1 passes through point A(1, –1,2) and is parallel to both planes P1 : x +…

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Q: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

A:

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² − 2x + 2y…

A:

Q: Find parametric equations of the normal line to *+ y? at the point (2, 2, 5) the surface z = O = 2+…

A: A detailed solution is given below.

Q: Find the real number a such that the line of x = 1, y = 2 – 1, z = 3 +t, parametric equations te R…

A: Given, parametric equations are                               x = t, y = 2-t, z = 3 +t, t in R To…

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

A:

Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

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Q: Suppose F(x, y) = x?i+ y?j and C is the line segment segment from point P = (-5, –5) to Q = (-3,…

A: Given data: The given expression for the vector is F→(x,y)=x2i→+y2j→. The given first point is…

Q: 1. Determine the vector component of A = 3a, + 2ag – 6as tangential to the cone. %3D

A: The vector is A→=3ar+2aθ-6aϕ. Generally, the vectors are shown as sketched below:   Instead of…