Find a vector parallel to the line of intersection of the planes 5x−y+2z=4 and 4x−y−3z=0v→=  (b) Show that the point (−1,−1,−1) lies on both planes. Then find a vector parametric equation for the line of intersection.r→(t)=

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

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Q: Find a vector parameterization of the plane 5x−4y−1z=18

A: By using prametrization

Q: ) Find a vector parallel to the line of intersection of the planes −4x − 2y + z = −7 and  5x +2y −…

A: (a) Given planes are −4x−2y+z=−7 and 5x+2y−5z=12 We have to find the vector v→ parallel to the line…

Q: 4 - x y + 1 %3D 2 1 3 L2 :[x, y, z] = [-2,4,3]+ t[-6, 5, 7], t E F

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Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

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Q: Find a vector n normal to the plane with the equation 5x - 5y – z = 10. n = (5,

A: Given equation of plane is 5x-5y-z=-10.want to find:Normal vector n to given plane.

Q: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

A: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

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: Determine a scalar equation for the plane that passes through the point (2, 0, -1) and is…

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Q: Find the equations of the normal line and the tangent plane to the parametric surface defined by the…

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Q: Find parametric equations for the line through the origin parallel to the vector 3j + 9k. Let z =…

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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: Write the scalar equation of the plane with normal vector - [0, – 1, O] and having a y-intercept 3.…

A: Equation of plane

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: Consider the curve C parameterized by f(t)=(t^2+2t+3,-2t-4,t^2-1),t E [0,+infinite[ a)Find the plane…

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

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: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 3 and…

A: Given plane equations are  x + y + z = 3 and x + z = 0. We have to find the intersection line…

Q: 2. Find the equation of the normal line and the tangent to the parametric surface defined by the…

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Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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Q: Determine the vector equation that represents the curve of intersection between the cylinder 2¹² +…

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Q: Two plane curves are defined by the vector functions r1 (t) = (t, 2t – 4) and r2 (u) = (2u, u²).…

A: r1t=t,2t-4 and r2u=2u,u2 For the intersection point, t=2u   ...1u=t22t-4=u2    ...2 Convert the…

Q: Find a vector function r(t) that describes the curve of intersection between the elliptical cylinder…

A: given, elliptical cylinder 4y2+z2=4  and the plane x+y=1 we have to find a vector function r(t) that…

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: The intersecting curve of two surfaces is given as follows:

Q: Find all points of intersection between the vector functionr(t) =⟨t, t2, t3⟩ and the plane defined…

A: Since the vector is contained in the plane, so all the points of the line intersect with the plane.…

Q: Find the Vector function that represents the curve of the intersection of the two surfaces.  The…

A: Given equations are x2+y2+4z2=4 ..... (1) and x2+z2=1 ..... (2) From equation (1) z2=(4-x2-y2)/4…

Q: Find equations of the normal line and the tangent plane to the parametric surface defined by the…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  compare coordinate on…

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

A: z=2x2+y2  & x=ey We can see that y can be represented in terms of x.

Q: Find the equation of the plane perpendicular to the curve r(t) = (cos(2t), t, sin(2t)) %3D at the…

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Q: A velocity vector of v = 3t²i – 6t³ j – 4k L is governing the movement of an object in the 3D space.…

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Q: Find a vector function that represents the curves of intersection of the two surfaces. 1.- The…

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Q: Consider the line perpendicular to the surface z=x^2+y^2 at the point where x=3 and y=2. Find a…

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Q: The position of a particle moving in the xy-plane is given by the vector (4t, y(2t)), where y is a…

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Q: Find a vector parallel to the plane 2x - y - z = 4 and orthogonal to i + j + k

A: Given:A plane 2x - y - z = 4 orthogonal to i + j + k

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: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

A: Let's find.

Q: Find a unit normal vector to the surface at the given point. x²y3 - y?z + 2xz3 = 4 (-1,1, –1)

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Q: Choose the normal vector of the tangent plane to the surface defined by z =e4x²+16xy-9y2 at the…

A: Explanation of the answer is as follows

Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

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Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

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 a scalar equation of the plane that passes through the points (1, 1, 1) and (2,0,3) and is…

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Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

A: First, we will sketch the curve of the intersection of the surface. The equation of the surfaces are…

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

A: The given curves are: z=4x2+y2     and     x=ey

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

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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 a vector parametrization for the quarter-ellipse from (5, 0, 6) to (0, −2, 6) centered at (0,…

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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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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.