2. Evaluate fadz, where C is a square with vertices -1±i, 1±i, traversed once in a counter clockwise direction.

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: ..... A= -1 1 is diagonalizable. Select one: True False

A:

Q: Find the cross product a × b where a = (0, 3, 4) and b = (5,1,2). axb =

A: Step 1: Step 2: Step 3: Step 4:

Q: onfiguration sh

A: The dual configuration diagram is given as,

Q: 1)calculate dedy ry where D is a parallelogram with vertices (0,0).(5,-1).(3,1) and (8,0) tip:Use…

A: Here we will use change of variable to find integral If we want to integrate f(x,y) over the region…

Q: Find the vertices of the triangle whose sides are the lines x = 0, x + y + z = 0, and 3x - 4y + 5z =…

A: Sol:- we need to find the points where these lines intersect.We'll denote the first intersection…

Q: Calculate v × w, where v = (−2, 1, 4) and w = (3, 2, 5).

A: Given: v = (−2, 1, 4) and w = (3, 2, 5)

Q: Find a b. . a = 8i + j, b = i-4j+ k

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Q: Let -4 -1 7 -11 3 -1 A 13 -1 1 -3 13 -1 1 -3 Find orthonormal bases of the kernel and image of A.…

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Q: Find the point P such that v = PQ has the components (-7.75, –8.25, – 16). О 3D (-2.75, -2.25, -6) P…

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Q: Find z,(-1,2) if z=In(5x°y²+2y*). Answer:

A: We can find the answer as below.

Q: Determine whether v = 3i - 5j and w = 6i - 10j are parallel,orthogonal, or neither.

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Q: Express w as a linear combination of u and v. 4 --}-}--[:] W = 6 u 3 2 6 6

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Q: z= 2e'+i

A:

Q: 13. Prove that the three points (-3, 2, 4), (6, 1, 2), and (-12, 3, 6) are collinear by using the…

A: To solve the following problem

Q: Prove that the points (-2, -1), (1, 0), (4, 3), and (1, 2) are the vertices of a parallelogram. Is…

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Q: Evaluate eリ+1 dA D where D is the triangle with vertices (0,0), (-1, 3), and (6, 2).

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Q: Determine whether v = -2i + 3j, w = -6i - 9j are parallel, orthogonal, or neither.

A: Determine whether v=-2i+3j,  w=-6i-9j are parallel, orthogonal, or neither. Solution:- if two…

Q: Plot the points in same three-dimensional coordinate system and determine whether u and v are…

A: The graph is shown below:

Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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Q: Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.

A: Given. A(x,5), B(2,3) and C(4,-5) are collinear.

Q: Write v as a linear combination of u and w, if possible, where u = (2, 1) and w = (2, -2). (Enter…

A: u=2, 1 and  w=2, -2To express v=4, -1 as a linear combination of u and w