[ Find r'(t) r" (t) given the following vector function. r(t) = (4²+2t)i + (51²+5t)j O 33 +164t 66+164t 33+82t 66+1641² 66+82t

Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

Q: Express the vector below in Cartesian coordinate: B = 2r sin cosc a₁ + r cose cose aer sind a ax=…

A: Given: The vector, B=2rsinθcosφar+rcosθcosφaθ-rsinφaφ   To express: The given vector in cartesian…

Q: Find the real values of ,a,b,c that make the convolution equal to zero for the vector function F(x,…

A:

Q: 4 В T(t+h) A 21 y 01 2

A:

Q: 1. Consider the pointsS= (1,−3) andT= (2,5).(a) Sketch the vector−→ST.(b) Give the component form…

A: Here 2 different problems are provided. As per our Bartleby Guidelines, we are supposed to…

Q: Let T: R² → R² be a reflection in the x-axis. Find the image of each vector. (a) (2,7) (b) (6, -8)…

A: T: R2 - >  R2 is a inear map which is basically reflection in the x Axis. Therefore for any point…

Q: ||ī|| = Find the length of the vector = 2 -2 Enter `sqrt(a)' for √Va

A: In this question we will find the Length of the vector.

Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

A:

Q: Vx+5 1. State the domain of f(x) = 10° using interval notation.

A: The given equation is

Q: Given A = x(2z -y) + ŷ(3x-2z) – 2(x+3y), find a unit vector parallel to A at point P =(-2, 1,–3).…

A: Vector valued functions are the rule that used to fix or associate a vector to a particular point…

Q: Let j = | and ü .Write j as the sum of two orthogonal vectors, it -2. %3D an {u} and ¤2 orthogonal…

A: Given:- →y=-69  →u=5-2

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

Q: Given ri = 3i - ej +In2 k, r2 = 5i + 7 e'j - 4 k and r3= 7i-7j+ k. Find the unit vector of (a)…

A:

Q: Find the vectors T, N, and B at the given point. r(t) = < t2, 2/3t3, t >, (4, 16/3, 2)

A: Step 1: Step 2:Step 3: Step 4:

Q: = ---- -2 8 span of v₁ and v₂? Let V₁ = and y = -5 -3 For what value(s) of h is the vector y in the

A: The given vectors  and .The objective is the find the value of  for which the vector  in the span of…

Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

A: The plane is perpendicular to the line, then the direction vector of the line is normal to the…