Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder x² + y? = a x (B) If ū and ỹ are two vectors then prove that ū can be written as a vector parallel to v plus a vector orthogonal to V .

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y2 = 50 and y? + 22 =…

A: Find a vector tangent to the curve of intersection of the two cylinderx2+y2=50 and y2+z2=50 at the…

Q: To compute h, (x) =*,+0,x,+0,*, in vectorized form then: (theta vector size is 1x3 and X is 3x1) (A)…

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Q: A. If x and y are orthonormal vectors, then find the valne of x+ yl? - |x-yl

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Q: Solve numerically for The scalar projection of vector u onto v

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Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1) and…

A: The vector parametrization is:                                       r(t) = r0 + tv = x0,y0,z0 +…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 3y+4z=−3 and 5x+y+2z=4

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Q: Verify Stoke's theorem for the vector point function yz2 (xz² .3 + ex over the surface S of the cube…

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Q: Find volume V(S) of the parallelepiped S in R3 determined by the (3,4,1); v3 following vectors: vị =…

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Q: Obtain a vector orthonormal to the vectors i−j  and (1, 0, 1)

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Q: The cross product of two vectors in R yields a scalar. True False

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Q: find a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8),…

A: The parametric equation of a line in vector for is given by the expression r→=u→+tv→. Here u→ is the…

Q: Find a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x²…

A: Idea  1) Solve the equation in term of only one variable (2) assume in term of parametric function…

Q: Find an equation of the plane. The plane through the point (8, 7, 1) and with normal vector 7i + j -…

A: The equation of the plane is given as:

Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: Find a vector of length 2 orthogonal to the plane 3x – 4z = 5. %3D

A: Here we have to find the vector of length =2 and  orthogonal to the plane 3x - 4z = 5 Let the vector…

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 two vectors of norm 1 that are orthogonal to the vectors u = and v =

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Q: The vector a in 3-space of length 3 lying in the yz-plane pointing upward at an angle of 5π/6…

A: let w= aiÌ‚ + bjÌ‚ + ckÌ‚   |w|= a2 + b2 + c2 = 1   W is lying in YZ plane and at an angle of 5π/6…

Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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Q: orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A: Here,        x = (3, 4)T       y = (-4, y2)T x and y is orthogonal if xTy = 0.

Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1)…

A: To find the vector parameterization for the line that passes through the point (1, 1, 1) and…

Q: Find an equation of the plane. The plane through the point (6, 1, 5) and with normal vector 5i + j -…

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Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (1, −1, 0), v = (0, 1, −1)

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Q: fx and y are two n-vectors, then prove that 1 1 -+-=1 (Holder inequality) (b) xy, <,, (Schwarz…

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Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=&lt;0,-2,1&gt;Hence, Vector…

Q: XII. Show that the dual vector of the antisymmetric part of the dyadic (1 2 3) Ā = 4 2 1 (1 1 1) is…

A: 1st calculate the antisymmetric part of the corresponding Tensor (matrix form). Then apply the…

Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

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Q: Show that the vectors a = 3i+ 4j and b = 4i - 3j are perpendicular. A smooth sphere A of mass 2m…

A: Consider the given: a→=3i^+4j^b→=4i^-3j^ mass M of sphere A=2m velocity of sphere A of mass…

Q: Find a unit vector n that is normal to the surface 4z? – 2x* – y = 18 at P = (1,2,3) that points in…

A: Solution of question is written in below steps.

Q: Prove: For nonzero vectors ū,vER, if (dot product) ū-v=0, then ū & v are linearly independent. Hint:…

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Q: 2. If A is the position vector of the point p-(x,y,z) and A=A. And ifr is the radius of the point in…

A: We apply the cross product to find the given function and simplification needed.

Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

A: The line integral ∫CF·dr involves the integration over a specific path. In this problem, the…

Q: 6.) Find a vector equivalent to the vector PQ with its initial point at the origin. = (;-2), Q =…

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Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = x^2 + y^2 and…

A: Intersection of paraboloid and cylinder can be obtained by representing y in the form x and z in the…

Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

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Q: Show with the help of the calculation rules for the scalar product for vectors ||x – 2 y|| = ||x||2…

A: The property used here are b2=b·b x·y=y·x cx·y=cx·y=x·cy Consider the left hand side of the given…

Q: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: Is it true or false that the vector u (3, 3, –3) is a normal vector to the plane -x – y + z + 3 = 0…

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Q: ) orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: Find two orthogonal vectors in the plane x + y + 2z = 0. Make them orthonormal.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

A: Given that, The vectors u and v are the vectors of the adjacent sides of the triangular region.…

Q: -) Are these pairs of vectors orthonormal or only orthogonal or only linearly independer [:]; » [] 1…

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Q: Find a nonzero vector normal to the plane z−3(x−4) = −4(1−y) correctly.

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 5z – (3x+3y) : 2 and 2x…

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