4) If u = 3y e, - xe, +5e,, v xe, +(y-z)e, and a = 5x - y+ yz Calculate a) u.v b) u X v c) VX v d) Va e) Va f) V.u

Q: Do only question 6

A: Evaluate fx​(3,1)Evaluate fy​(3,1)Find the derivative of f(x,y) with respect to x, treating y as a…

Q: Let A=(1, 0), B=(0, 1), C=(1, 1), and D=(r, 1). Verify that R(A, B, C, D) = r.

A:

Q: Find u. v, uu, ||u||², (u - v)v, and u . u = , V = (a) (b) u. V u . u (c) || u ||2 (e) (d) (u. v)v…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 6. Find UV (dot a) Ū · V = (2, 3, -

A:

Q: m) Linearize : -3x 天ェ_= around %31

A:

Q: a) Find ū - i b) Find w.u 1/2

A:

Q: Consider the vectors u=(2,3,-5), V = (-3, -2,6) and w=(-4,8,4). Calculate u.v

A: We have to find u.v

Q: 11. Given vector u = (2, a, 3), vector v = (1, -3, b) and u x v = (13, -5, -7). Find a and b.

A:

Q: Write v (2,5, –4,0) as a linear combination of uz = (1,3,2, 1); U2 (2, — 2, -5,4); из %3D (2,…

A:

Q: 4. If w = x²y + y²z + xz², show that дw Әх дw дw дz = (x + y + z)2.

A:

Q: 4. Given vectors: =(4,9), v = (-8, 15) and w=(2, 10) a) Show that and w can span R².

A:

Q: 7. Find the centroid of a triangle whose vertices are (2, 3), (-4, 6) and (2, -6). В. (0, -1) A. (0,…

A:

Q: If u=(2,4)�=(2,4)  and v=(3,−4)�=(3,−4)  then proju(v)≈

A: The objective of this question is to find the projection of vector v onto vector u. The projection…

Q: 27. Determine the area of the parallelogram formed by the vectors u=[3,-2,5] and v=[-1,4,2].

A: Step 1:

Q: The point (1,2-1) in space is inside the ball B((1,1,1);2).

A:

Q: 5) Which linear function represents the graph given? A) x-3y 12 B) x+3y = 12 C) 3x+ y = 4 D) y= -4…

A: Graph of the linear function is given, we have to find its equation

Q: Find the angle in degrees between u = (1, 2, 0) and v = (1, -2, 1)

A: Given, u=1,2,0v=1,-2,1 The formula for finding the angle between the two vector is, cosθ=u→·v→u→v→

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: Find the value of y, given the value of x. 11 a) Cari nilai dy dengan nilai x yang diberikan. de de…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 10. Let ā = (1,2) and b= (2,1). Find projz(ā). Then show that ā– projz(ā) is orthogonal to b…

A:

Q: Find u (v x W). u = (3,3,3) (5,9, 0) V = w = (0, 0, 3)

A:

Q: 21. Given vectors u = (1,3) and v = (-6,2). a) Find u - 3v b) Find Ju + v].

A:

Q: 15) Find u x v for u = and v = .

A: Given vectors are, u = -7, 1, 12 = -7 i^ + j^ + 12 k^v = 2, 2, 3 = 2 i^ + 2 j^ + 2 k^

Q: 21. Determine if each vector equation represents the same line as l1 : [x, y] = [-3, 5] + {[1, –4].…

A:

Q: Exercise 1) ỷ + 3ỳ + 2y = 36xe*

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.