20. Which of the following vectors is normal to the surface In(x + y* -- z) = x-1 at the point where y-8 and z = 4 A) i-j-2k B) 2i-3j+k C) i+2j D) -2i+ j+3k E) j-3k

Q: Find the normal vector to the plane that contains the point (1, 1, 3) and the line r(t)=(0,1,…

A: Let P be the point 1,1,3.Q be the point 0,1,2 on the line.Then, PQ→ = 0-1,1-1,2-3=-1,0,-1And the…

Q: . Use a cofunction relationship to show that the product (tan 1°)(tan 2°) (tan 3°)· .…. ·…

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Q: Q3. Find out values of a, b, c for which curl of vector V is zero, where V = (2xy+ 3 yz) i +(x² +…

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Q: Find the scalar equation for the plane passing through the point P=(−5, 3, 2) and containing the…

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Q: For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax…

A: Correct last vector coordinates representation

Q: Is the vector parallel to the plane x+2y+z+4=0? Explain why?

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Q: Q/Find the real values of a , b, c that make the convolution equal to zero for the vector function…

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Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

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Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: Consider the three following points of R'. A = (0, 2, 2) B = (1, 1, 1) C = (-1, 1,2) (a) Find the…

A: The scalar equation of a plane is of the form: ax+by+cz+d=0, where a, b, c ,d are constants. The…

Q: Find a set of vectors {ü, ī} in R' that spans the solution set of the equations w - 1 - 2z 1 5w + 2z…

A: The objective is to find the the set of vectors that spans the  solution set of the equation.

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: Find the vector equation for the line of intersection of the planes 5x + 4y + 5z = 1 and 5z + z = -4…

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Q: Find vector and parametric equations of the plane that contains the two intersecting lines † =…

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Q: 3. A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A…

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Q: The planes α and β in R 3 are given via equations α : x + 2y − z − 2 = 0 and β : 2x − 2y + z − 1…

A: We find required equation of plane in given form.

Q: Find the equation of the plane that contain point A(3,1,4) and line I given parametrically as T(L) =…

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