= In(x°y®) + x2 Consider z as a function of the variables x, y which is denoted by z = and let P(1,-1) be a point. Consider further the vectors u = (a, B), w = (-a. B), such that ||u|| = V73. 79/73 97 73 Duz(P) = 73 Dwz(P) If %3D and determine: 73 The value of a:

Q: Let L be the line passing through the point P(1, 1, 1) with direction vector d=[2, 1, 0]T. Find the…

A:

Q: Let L be the line through the point Q = (-2, 9, -4) and direction vector -[-1, 2, -2]T. Find the two…

A: The equation of the line passing through the point x1, y1, z1 and having direction ratios l, m, n is…

Q: Let Z be the line through the point Q = (4. 6. 2) and direction vector -[1. 2. 2]T Find the two…

A:

Q: (a) Let v, = and V3 = 2. -9 - Express v as a linear combination of those vectors. 8. Let v = 8 V =…

A: Here we have to find the vector.

Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

A:

Q: F(x, y, z) = (z sint z sin(ar), e²y-2 X b+y

A:

Q: Let C = (-2, -1) be the center of dilation. Let X = (1, 1), Y = (3, 0) and Z = (2,5). Our dilation…

A: Center of dilation=-2, -1X=1, 1, Y=3, 0, Z=2, 5Dilation factor, k=3

Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

A:

Q: Let l be a straight line that passes through the origin and is parallel to the vectors…

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

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

A:

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: Determine Duf(-1,3, 2) for f (x, y, z) = e2ay° + 4x²yz in the direction (3, -2, 5). V =

A:

Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

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: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

A:

Q: Q1. If the components of a contravariant vector in (x') coordinate system are (3,4). Find its…

A: 1) Given information: x¯1 = 7x1 - 5x2x¯2 = -5x1 + 4x2 The components of contravariant in xi…

Q: Let I be the line passing through the point P=(3, -2, 1) with direction vector -[3, 2, -3]T. Find…

A: If we drop a perpendicular from a point P on a line  l then foot of perpendicular will be closest…

Q: Show that t, e^t, and sin(t) are linearly independent.

A: In the given question we have to show that t, e^t, and sin(t) are linearly independent.