Determine the area of AABC if A = (2, 1), B = (5, 3), and C is the reflection of B across the x axis.

Q: 60. Show that the distance between two points P1(x1, y1) and P2(x2, y2) is invariant under rotation.…

A: For the points P1 and P2 , the distance between the points is given d(P1,P2)=(x2-x1)2+y2-y12 . For a…

Q: On a plane equipped with a polar coordinate system, what is the area of ​​the triangle with vertices…

A: In polar coordinate system x=rcosθy=rsinθ

Q: e.) (17, ), (–17, ) 86л 3 3 t.) (2, 14т), ( —2, 14т)

A:

Q: If a point, P1=[10,10,10], will be rotated by 60 degree about the Z-axis, find the final position…

A: Solution ) suppose P1 [ x1 y1 , z1] is rotated about z axis so new point P2 [ x2 , y2 , z2 ] is…

Q: 2. Demonstrate the following relationship involving the dot product and cross product (a) u. (v xw)…

A:

Q: Hiw.2 Censider the PakullelePifed with šider: A=3i+2j+k Bziti+zkyczi+sj+3k;. thens t-Find the…

A: Given

Q: trength, S ot S: Kxy? where K x and y or the stron a beam 2

A: Given:- Strength (S) of the beam is given by  S=Kxy2

Q: 20b. Find the coordinates of A' after A(-3, 4) has been reflected: Reflection in the x-axis: A'= I…

A: To find the reflections

Q: Change into polar co-ordinates S Va²-x2 Lzdydx, and evaluate.

A: From the given integral: I=∫-aa∫-a2-x2a2-x2dydx The limit of integral, clearly shows that y varies…

Q: 2. Demonstrate the following relationship involving the dot product and cross product (a) u. (V x W)…

A: a) To prove .c) To prove .Concepts Used:Commutativity for Multiplication: Commutativity for…

Q: Create an application (different from any found in the text) that requires a dot product.

A: The application of the dot product is to find the angle between two vectors. Let us consider two…

Q: Prove that for A # B, AB S AB S AB.

A:

Q: Find midpoint M of P,P2, which joins P1(5, -7, 2) and P2(2, 5, 6), as shown in Figure 10.46 of…

A: Formula used : Mid-point formula Mx1+x22,y1+y22,z1+z22 Here (x1,y1,z1) and (x2,y2,z2) are the end…

Q: et D be the triangle with vertices (0,0), (1,0) and (0, 2). Compute ffp (e2y + 1) dA.

A: Given is the triangle D with vertices 0,0,1,0,0,2 The objective is to evaluate the integral ∫∫D…

Q: 1. The shape function for the two dimensional rectangular element in Figure 1 are: N₁ N3 1 4ab 1 4…

A: As per the question, we are asked to find the Jacobian matrix [J], its determinant |J|, and the B…

Q: 个5 ) Draw AND LABEL A A'B'C' THE IMAGE OF A ABC AFTER REFLECTION OoVER THE X-AXIS. A(2,1), 8(5,1), c…

A: Part (a) Given coordinates of vertices of triangle are A=2,2B=5,1C=4,4

Q: 3. Show the parametric form of the line that passes through points A(3, 6, 1) and B(2,10, 5) Compute…

A:

Q: plot the point given in polar coordination (3,-3π/4). find three aditional polar representation of…

A: This is a problem of polar to cartesian conversion and the idea of parametrization.

Q: True or False: The point H is collinear with both C and E. B D G True False

A: any number of points are called collinear if they all lie on same straight line.

Q: . AABC with A(3, 4), B(-1, 0), and C(-2, 4) reflection in the line y = x.

A: First draw a triangle ABC with given vertices and a line y=x, through which we will reflect triangle…

Q: are the following points collinear? show your calculation A( 0,10) B(3,4) C(-5,20)

A: We have to check

Q: Let A = (1, –1, 2) and B = (4, –2, 3). Solve for proj,B. %3D

A: As per the guidelines for the multiple questions I had solved the first question.

Q: Calculate the cross product. (i - 9j + 6k) x (j – k)

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Q: Make a general statement regarding invariant points after a reflection in the x-axis and then in the…

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Q: (b) Let w = 1+ j. Determine w giving your answer in rectangular form.

A:

Q: What is the location of the image of P(−8, 1)P(-8, 1) after a counterclockwise rotation of 90°90°…

A: Given: Point P-8, 1. To find: Image of the point P after a counterclockwise rotation of 90° about…