2. Determine whether the following vectors are linearly dependent in R³: (O)--- ()--C) 1 , = , ez = 0 0 0 1 (a) e₁ = 0 2 ·()· · - () -- () --- () -- () 2 , V = W = (c) u = V= 2 1 1 1 -2 (b) u = (d) u = (-)--(-)--() 2 V= W = 0 6 -3 6

Q: 13. Find a vector equation of the line through (2, 1) parallel to (x, y) = (-2,7)+t(3,5). 14. Find a…

A:

Q: Let B be a subset of R4. Which of the following statements are correct? If |B| = 5, then B spans R4…

A:

Q: Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: Suppose f(x, y) = (a) ▼ f(x, y) = (b) ▼ f(-0.7, 7) = tan(x) + y and u is the unit vector in the…

A: Given that f(x,y)=tan(x)+y  and u is the unit vector in the direction of <2,3>now, ∇f(x,y)=fx,…

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: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: Suppose f(x,y) = = tan(x) + y and u is the unit vector in the direction of (-3,-1). Then, a) ▼ f(x,…

A:

Q: A vector equation for the line through the points A (3, -4, -3) and B (3,4,2) is (x, y, z) = . (You…

A: Concept to be used:If a line passes through two points A,Bwith position vectors aand brespectively,…

Q: 5. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = (5) and pue (4 E)=

A:

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·A·B·0-0-0-0 x 3 +y -2 +2 1 = 1…

A: We want to find values of x, y and z which satisfy given equation.

Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

A:

Q: Suppose temperature °F in a region of 3-space, measured in meters, is given by T= 100 1+ (x − 3)² +…

A: Given: T = 1001 + (x+3)2 + y2 + (z+2)2 Where T is the temperature function. Position of the bug =…

Q: Find a set of vectors {ü, ī} in R' that spans the solution set of the equations w - 1 - 2z 1 5w + 2z…

A: The objective is to find the the set of vectors that spans the  solution set of the equation.

Q: s the set of the vectors (:). (2) 1 ) --(;) --() u2 4 U3 = 1 1 1 rthogonal? What is the expression…

A:

Q: Determine whether or not the 3 vectors of P2(R), p1(t) = 1−t², p2(t) = t, p3(t) = −1+t+t² arly…

A:

Q: Suppose f(x, y) = (1, -3). Then, (a) Vf(x, y) = (b) Vƒ(1,5) = (c) fu (1,5) = Du f(1,5) = x² + y² and…

A:

Q: Let u = (2, 1, -2), v= (0,3,-5), and w = Compute the indicated vectors. (a) u × v = (?, ?, ?) (b) -…

A:

Q: In R, evaluate the alternating 2-form 5 = -3 · dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: In ℝ3, we have to evaluate the alternating 2-form ξ=-3·dx∧dy on the pair of vectors (a,b). a=4,2,12…

Q: b) u = (3, -1), v = (1, 5) et w = (8, -2) c) i = (1, 0, 0), j = (0, 1, 0) et k = (0, 0, 1) gajte…

A:

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

A:

Q: Where does the line with the vector equation [x,y,z] = [6, 7, -8] + t[-2, 4, 1] intersect the…

A: