For the given vector function below, find the equation of the plane that contains the osculating circle . = (t,2t²,t³), t= 1 6x - 2y +z = 6 а. b. 6x - 3y +2z = 2 с. 6x + 4z = 10 d. 12x - 2y +z = 9 6х - 2y +2z%3D4 е.

Q: Find the vector form of the equation of the line inR3 that passes through P = ( -1, 0, 3) and is…

A: Equation of a line passes through  x1, y1, z1 having direction ratios a, b, c is, x-x1a=y-y1b=z-z1c

Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – = =11 and 4x + 2y – 3= =…

A: Topic:- vector

Q: Use the component form to generate an equation for the plane through P1(4, 1, 5) normal to n1 = i -…

A: Recall the following fact.

Q: Find a vector parametrization of the line through P = (3, –8, 5) in the direction v = (-2, 0, 3)…

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Q: Find the vector equation for the line of intersection of the planes 5x +y-3z= -3 and 5x + z = -1 r =…

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Q: The of a moving Position Vector 3/2 point in space is given by 212 t RCE) =t cost i + tsint J +…

A: According to the given information, Consider the given position vector:

Q: The surface of a hill is modeled by z = 100 – 3x? – 4y². When a group of hikers reach the point (1,…

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Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: Topic = vector

Q: Find the vector equation for the line of intersection of the planes x + 4y + z = -5 and x + 4z = 0…

A: Here we have to find the vector equation for the line of intersection of the planes x+4y+z = -5 and…

Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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Q: Find the vector equation of the line of intersection of the planes x+y+z=1 and x+2y+2z=1.

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Q: Find the length of the curve with the given vector equation. r(t) = 2t 4 1 + 11t j+ 10t 4 k, -1 sts…

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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 the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 –…

A: Let's find.

Q: Find parametric equations for the line whose vector equation is given. (а) (т, у) 3 (6, —5) + t(1,…

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Q: Find the vector equation for the line of intersection of the planes 32 + 2y :0 ánd 3* + ,0 ) +t(6, r…

A: To find the equation of line intersection of given planes.

Q: Given the vector function 7 (t) = (2t, – 2t°, 5t° + 3) Find the velocity and acceleration vectors at…

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Q: Find a vector normal to the plane with the given equation. 2x + 8y + 9z = 3 n =

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Q: the vectors y₁, y₂, Y3 (where y; E R² V i) must be linearly dependent?

A: Given the vectors y1, y2 and y3 in the vector space R3.

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

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Q: Find an equation of the plane. The plane through the point (4, 0, -5) and perpendicular to the…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

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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…

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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: Evaluate /1+ x² + y°dS, where S is the helicoid with vector equation S r(u, v) 0 < u < 3, 0 < v <…

A: Given integral ∬S1+x2+y2dS, where S is helicoid with vector equation r^u,v=ucosv,usinv,v We have to…

Q: b) Find the center and radius of the sphere x+y+z6x+4y-10z+25%=D0. C) Compute a ·b, axb, and…

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Q: find the two-dimensional vector equation of the line r(t) = a +t*m such that - r(0) has norm 8 and…

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Q: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

Q: Given the vector function 7 (t) = (3t, 5t", – 3t° + 2) - Find the velocity and acceleration vectors…

A: Given that vector function r→ t=3t,5t2,-3t5+2 To find the velocity and acceleration at t=-1Solution…

Q: Find the vector equation of the line of intersection of the planes x+y+z = 1 and x+2y + 2z = 1.

A: The equation of the line vector of the intersection of 2 planes can be calculated using the cross…

Q: Find the general form of the equation of the plane passing through the point and normal to the…

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Q: Evaluate 1+ x² + y*dS, where S is the helicoid with vector equation r(u, v) 0 < u < 2, 0 < v < 2T

A: Given ∬S1+x2+y2dS where S is the helicoid with ru,v=u cos v, usin v, v, 0≤u≤2, 0≤v≤2π. Since ru,v=u…

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: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

Q: Given a the vector equation r(t) (4 + 4t)i + (1 + 1t)j + (1 + 4t)k, rewrite this in terms of the…

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

A: z = 4x2 + y2  ,  y = ex    We observe that the given two equations, here we can see that y can be be…

Q: Find the velocity, acceleration, and speed of an object with position vector r(t) = (Vi, 4 + Vi,…

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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: Find the vector equation for the line of intersection of the planes x – 5y + 2z = 1 and æ + z = 1 |…

A: To find the vector equation of the line of intersection of given planes.

Q: Find the velocity and acceleration vectors for the motion described by x = 4 – 3t2, y = 4 – 5t, z= 9…

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Q: Sketch the curve with the vector equation 7(t) = (t,2 – t, 2t). Indicate with an arrow the direction…

A: Solution

Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

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Q: EX -Find the. vecter.projechun.f 6+3j+2k enbo T=i-2j-2k and. the scalar.Campenout.of.in.. the…

A: Given data: The first vector is u→=6i+3j+2k. The second vector is v→=i-2j-2k. The expression for…