Find a vector tangent to the curve of intersection of the two cyclinders ? + y² = 98 and y² + z² = 98 at the point (–7, –7,7). O 196i+ 98j+ 196k O 196i+ 196j+ 98k O-196i + 196j + 196k O -98i+ 196j+ 196k O 147i+ 196j+ 196k

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Q: Q2: (a) Find the scalar and vector projection of ū along ủ, where u¯=(2, 3, 4) and v¯=(2, 2, 0). (b)…

A: Given : u=2,3,4, v=2,2,0 we know that scalar projection of u along v is given by…

Q: Find the image of the vector (1, 1, 1) for the given rotation. 60° about the z-axis

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Q: Find all values of t for which the tangent line to the curve r(t) = (2t – t,t - t²) is orthogonal to…

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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: 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 an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

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Q: find T, N, and B for the curve at the indicated point. Hint: After finding T', plug in the specific…

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Q: Find a vector parametrization of the curve x = -3z² in the xz-plane. t as the parameter in your…

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Q: Find a vector function that represents the cur ve of intersection of the paraboloid z a + mnd the…

A: Given that, the paraboloid is z=x2+y2 and the cylinder is x2+y2=22. The projection of the of the…

Q: Let u=(-1,37 and u =< 2,-57 Find the Component form of the vector Su-V

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Q: 6. Compute the Divergence and Curl of the following vector F:F = yze#vi + xze#¥j+(e™y + 3 cos 32)k…

A: Use divergence and curl formula Compare hyperbola with standard equation of hyperbola

Q: Which of the following describes a plane perpendicular to the vector n = (2, 1, -4) and contains the…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y? = 8 and y? + 22 = 8…

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Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

Q: Thẻ nòrmal vector to the plane 3x + 4y – 5z – 6 = 0 is A 3i+ 4j – Sk B 3i + 4j + Sk C 3i+ 4j – 6k D…

A: It is normal vector form.

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…

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Q: 19. Supposethat the normalunit vector N of a surface S at z = f(x,y) is determined, how does the…

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

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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 x such that the vectors xi+2j -3k, i+j ,j+3k are Coplanars (lies the Same Plane) . on

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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).

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Q: Find the vector parametric equation of the line that passes through the points P(6,–2, –1) and…

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Q: 4. (a) Find the mid-point, unit tangent vector and unit normal vector at the mid-point of a planar…

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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 a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: 6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the…

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

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Q: Find the point on the graph of z = 2x^2 − 3y^2 at which vector n=⟨8,−12,1⟩ is normal to the tangent…

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Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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Q: Q4: Find the vector projection of u 6i + 3j + 2k onto v =i- 2j 2k and the scalar %3D component of…

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Q: Let W be the union of the second and fourth quadrants in the xy-plane. That is, let W= Complete…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders a2 + y? = 8 and y² + 22 = 8…

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

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Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: Find the scalar equation of the plane that passes through point P(−3, 3, 5) and is perpendicular to…

A: To Find: Scalar equation of the plane that passes through point P(−3, 3, 5) and is perpendicular to…

Q: Find an equation of the plane that passes through the point P(4, 5, 3) and has the vector n = (1, 8,…

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Q: 2.) Consider the fallowing V= (-1,1,1,0) 0.) Find the standard mo trix A for the linear tronsformaie…

A: The given Linear transformation is,Tx1,x2,x3,x4=x1-x2, x3, x1+2x2-x4, x4

Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero