Exercise. The position vector for the curve C in the (, y, z)-space is given by r (t) = (2t + 1, t² , 3t). Find values for the constants a and b so the curve C lies on the surface x2 – 4y + az = b or explain why no such constants exist. Are there values for a and b for which the curve lies on the surface? yes ? Check work no

Q: Find the equation of the tangent plane to the surface z =9-(r² +y2) at the point (1,1,7). Write the…

A: Given surface is z=9-x2+y2⇒x2+y2 +z=9⇒x2+y2 +z-9=0 Take  fx, y, z= x2+y2 +z-9 And, Point say P is 1,…

Q: Q4. Find an equation of a plane that contains the line x=t, y=1+2t, z=2-t.

A: We have to find the equation of plane .       According to our guidelines ,we cannot solve all…

Q: u = (2, 3) and v (-6, 4). (a) Find u -3v. (b) Find u + vl. (c) Find u· v. (d) Are u and v…

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Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

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Q: Let T, denote the plane parallel to the xz-plane through the point (1, 2, 3). Let n2 denote the…

A: To solve this problem first of we find the equation of the plane π1 and π2 in standard form and then…

Q: Find the d. c. of T from definition.

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Q: Sketch and identify the surface given by x2 + 4y + 4z2 = 0.

A: Equation of the surface is given by:x2+4y+4z2=0 we need to identity the surface and hence sketch the…

Q: classify and sketch the surface given by x2+2y2+z2-4x+4y-2z+3=0 (indicate the vertex coordinate)

A: Here we have given a surface equation as below:  x2+2y2+z2-4x+4y-2z+3=0 The surface given by the…

Q: 16. Consider the equation of the surface S given by z = 3r*ya + 3y – 4 Where a is an even number and…

A: Linear approximate equation is the equation of tangent plane.

Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

A: To find the coordinates of all points on the surface where the surface has a horizontal plane, we…

Q: Consider the function f(x, y, z) = 3x² + y² - 4z. i) A contour surface S passes through the point A…

A: To find the value of the contour surface passing through the point A = (2, 3, -1), we need to…

Q: Find parametric equations for the line through (1,10,-3) perpendicular to the plane 10x+3y+5z=19.…

A: Solution=> A vector perpendicular to the plane ax+by+cz+d=0is given by (a,b,c) So a vector…

Q: Find an equation for the surface that contains all such points that has equal distance to the point…

A: This problem is from analytical geometry. To solve this problem I have used distance formulas.

Q: Write an equation for the level surface of f(x, y, z) = r² + 10y? + 20z2 corresponding to the level…

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Q: Using following result find a set of parametric equation of the line. x=x1+t(x2-x1), y =y1+tV2¬y1)…

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Q: Find equations for (a) the tangent plane and (b) the normal line at the point Po(1,2,2) on the…

A: Given, surface is , point is .

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

A: 1. Point : S2,-3,4   Plane : x+2y+2z=13   2. Point : S0,-1,0   Plane : 2x+y+2z=13

Q: nd a set of parametric equations for the line passing through the point (1, 0, 9) that is parallel…

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Q: The Line whose eduation is (X + 2y +Z=!) > Cx -y + 2Z +7 =0) intersecks X Z plane. write equation of…

A: The line represented by the equation x+2y+z=1 and x-y+2z+7=0 intersects the XZ plane.

Q: 4 /5 . 135% + - (a) Find parametric equations for the line of intersection of the planes x+2y- = 3…

A: In X plane, put y=z=0 & in Y plane put x=z=0 &in Z plane put x=y=0

Q: Find parametric equations for the line through the point (0, 1, 2) that is parallel to the plane x +…

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