Give a set of parametric equations for the line L4 that lies tangent to the graph of the vector function F10) = (e*-4 -3, V=21) ..uil (7, –2) to (-3, 3). at the point (1, –3, 2).

Q: At which point P does the curve r(t)=( 2t, 4t+1, t’) given in vector form have the tangent vector…

A: Given: To explain the correct option of the given statement as follows,

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: What is the parametric equation of line through the point (1,2, -1) and perpendicular to the plane…

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Q: Find a parametrization of the line passing through (2, 0, 4) and (4, 1, 2). r(t) =

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Q: .3 At which point P does the curve r(t) = ( 2t have the tangent vector (24, -8, 3) ? (a) P(2, 2, 2)…

A: Here we have, the given curve is r→(t)=2t3, 2t2, 3t-1                now differentiate with respect…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: As per given by the question, there are given: a→t=6t, 5sint, cos6tv→0=4, 3, 5r→0=3, -4, -4 Now, For…

Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

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Q: Let P be the point (1, 1, 4). Find the parametric equations of the line through P and parallel to…

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Q: Sketch the curve of the vector function r(t) = 3ti+ (3t + 1)j,-1<ts2, and indicate the orientation…

A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at the…

Q: Find the parametric equations of the tangent line to the curve represented by the vector function…

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Q: Find parametric equations of the line through (-1,0,3) that is parallel to 5i – 6j+k. x(t) y(t) =…

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Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x= 2+3t y…

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

A: To indicate the direction in which t increases and sketch the graph of the vector function given…

Q: The planes 4x + 4y + 3z = -15 and y - 5x - 2z = 11 are not parallel, so they must %3D intersect…

A: Given: The planes 4x+4y+3z=-15 and y-5x-2z=11

Q: Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0…

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Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² – 2x + 2y…

A: The given equation is: 2x2+2y2-2x+2y=7...(1)

Q: Find the vector parametric equations of the two straight lines tangent to the given space curve

A: Given,              rt=2t2+3i+15t-7j+4t2+5kand  passing through the point P-3, -22, -7.

Q: Find the parametric equations for the lines. Where, the line through the point P (3, -4, -1)…

A: Topic = Vector

Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

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Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

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Q: At which point P does the curve r(t) =( 2t2, 4t+1, t³ ) given in vector form have the tangent vector…

A: Given, r(t)→=2t2,4t+1,t3  tangent vector 4,4,3 we know derivative of vector valued function gives…

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: Find the parametric equation for the line in R' that passes through the point (1, –2, 3) and that is…

A:

Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

A: For the solution follow the next steps.

Q: 1 - Find a vector equation and parametric equations for the line segment connecting P(a, b, c) and…

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Q: Q2. A point is moving along a curve whose position vector is Find : the acceleration components at /…

A: Consider the given position vector

Q: A point, p, is moving with acceleration 6t j - k at time t. If at t 1, the coordinates of P are (1,…

A: Answer

Q: Express the given parametric equations of a line using bracket notation and also using i, j. k…

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Q: For time 1 > 0, the position of a particle moving in the xy-plane is given by the parametric…

A: Velocity==rate of change of distance per unit time=displacementtime=dsdt. Given that: x=4t+t2  and…

Q: 7(t) =

A:

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t), sin(3t), cos(3t))…

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Q: Write down the vector equations of the tangent lines to the traces for /(r, 3) = re-y² at (2,0) for…

A: To write the vector equation of the tangent line for the below function to the trace y=0.…

Q: 4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x -…

A: Given plane is, 2x-3y+7z-4=0

Q: Match the parametric equation with the corresponding plane curve displayed. Sx=47-5 y=16 130 104 78…

A: The given parametric equation is: x=4t2-5y=16t4

Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

A:

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 The unit Vectors tanent and normal to The ellipse x+2y= 6 at The Point (2,1).

A: Given, ellipse x^2+2y^2=6   point=(2,1)

Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

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Q: Find the parametric equations of the tangent line to the curve represented by the vector function 7…

A: Topic  = Vector

Q: At which point P does the curve r(t) = ( 2t+3, 3t², t* ) given in vector form have the tangent…

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Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: The unit vector tangent to the curve r(t) = (1,41*,3r*) is (a) (0,4/5,3/5). (b) (0,81,6t)

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Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: Find the distance of the point (2, 6, –4) from the line r(t) = (-1 + 31, –1+41, 5 – 2t). Give a…

A: Consider the given point as, 2,6,-4  And the line -1+3t,-1+4t,5-2t

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: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² − 2x + 2y…

A:

Q: Find a set of parametric equations for the rectangular equation that s y = 2x – 3, t = 0 at the…

A: let x = t + a put all the given points to find out the value if a x = 4 and t = 0 4 = 0 + a a = 4 so…

Q: At which point P does the curve r(t)=( 2t³, 21², 3t – 1) givenin vector form have the tangent vector…

A: According to the problem, we have

Q: Find the parametric equations for the line of the intersection L of the two planes. 6x – 3y+ z = 5…

A: Parametric equations of the line is :  x(t) = x0 + a t  y(t) = y0 + b t  z(t) = z0 + c t  Here ( x0…

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.