Let w = (x° + y) dæ + z dy + (x + y°) dz and n = 5 dx + (z – 5) dz. :- Find the wedge product w A N. w^n= |dy ^ dz + dz A dx+ d Λ dy

Q: Find the dot product of x = 5 and y = 0 x.ÿ= 2 ི ༠༠

A: Step 1:Given to find the dot product.For vectors of form ⎣⎢⎡​x1​x2​x3​​⎦⎥⎤​ and…

Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

A:

Q: (x- 2y) dA on the parallelogram P bounded by y = 5 – 2x, y = 7- 2x, y = 3x – 6, and y = 3x + 2. Use…

A:

Q: Find the cross product i x v where i = 2i +2j -3k and i = (- 8, – 6, 3). i x ở =

A:

Q: If C is the line segment connecting the point (a1, b1) to the point (a2, b2), show that 3r dy – 3y…

A:

Q: Find the (a) dot product A B and cross product B x -A if A = 12 in directed at 33' and B = 16 in,…

A: Here we use the dot and cross products formula in terms of length and angel.

Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

A:

Q: Let x=x= and y=y= Find the dot product of xx and yy.     x⋅y=x⋅y

A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

Q: Evaluate (x + y)ds where C is the straight-line segment x = 4t, y = (12-4t), z = 0 from (0,12,0) to…

A: Let  where C is straight line segment  from .We know thatwhere

Q: Let a = (5, 4) and b = (5, – 8). Compute the dot product. a b

A:

Q: the diagram: ΔLMNΔLMN  is a right-angled triangle with vertices L(−6;7),M(a;b)L(−6;7),M(a;b) and…

A:

Q: Use the substitution u = x² and the equation of a semicircle to evaluate 4XV4 - x* dx.

A: Given the integral  I =∫024x 4-x4dx To evaluate the integral :- Using the substitution,  u = x2  du…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and…

A:

Q: Find the values of w, x, y, z and Dx x + y + z + w = 13 2x + 3y - w = -1 -3x + 4y + z + 2w = 10…

A:

Q: Imagine a triangle △ABC where A(−53,−60,−49), B(−102,−98,−107), and C(3,6,5) is in 3D space. A point…

A:

Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

A:

Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

A:

Q: Let y = d -7 = 7 and u = -7 -2 Compute the distance d from y to the line through u and the origin.…

A: Introduction: Let l be the path connecting the origin to u. We can compute the projection of y onto…

Q: A rectangle ha verices at P (6, 6), Q (6, -6), R (-6, -6) and S (-6, 6). The origin is the center of…

A:

Q: Compute the Jacobian for the substitutions x = ρsinφcosϴ,  y = ρsinφsinϴ,  z = ρcosϴ.

A:

Q: Evaluate F. dr along the line segment C from Pto Q. F = -8 xi+5y j; P(-1,0), Q(7, 0) F. dr i

A:

Q: Find the area of the triangle formed by the points A = (3, –1, 2), B = (1, 1, 0), and C = (1,2,–1).

A:

Q: Find the distance d between the two parallel planes x + 2y 2z = −2 and x + 2y = 2z = 1.

A:

Q: Find the cross product a x b. a a = (t, t², t³), b = (1, 4t, 9t²)

A: