1. Use the following diagram to prove analytically that the diagonals of a rhombus are perpendicular. B (a, b) a A (0,0) Z C D(a.o) c'

Q: b. Find the projection of v with equation 2x -y + 4z = 0. 1 -3 on the plane

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Q: #1. The area of the parallelogram spanned by the vectors v = (A) – 22 (B) 22 (C) 23 (D) 8 (E) 2 (5,…

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Q: The plane with equation:

A: Given, the plane with equation:                        r→=(1, 2, 3)+m(1, 2, 5)+n(1, -1, 3)…

Q: how the condition that the curves a+b=1 and d+b'

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Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

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Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: a) If Jä| = 2, JB| = 3 and the angle between å and b is, find the length of å- 2b. %3D %3D

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Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: Are these points collinear? a) A(-1, –2), B(3, 2), and C(5, 5) b) D(a, c – d), E(b, c), and F(2b —…

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Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

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Q: iven two line segments, construct a rhombus whose diagonals have lengths equal to the lengths of the…

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Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

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Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

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Q: 2. Assume that the plane P3 is perpendicular to the yz-plane, and the line l2 : x = 2t, y = t, z =…

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Q: 3. A player P stands 10 metres directly in front of a soccer goal O ABC, as shown below. The corners…

A: a)Co-ordinates of GG0+7.52,0+02,0+02=G154,0,0Co-ordinates of P∵P lies on the  xy planeso…

Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

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Q: Suppose C is the triangle with vertices (3, 0, 0), (0, 4, 0), and (0, 0, 1) oriented…

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Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→

Q: In ARST, SV bisects y ZRST. Find the coordinates of point T in terms of a. S (a, a) 2a T?, ?) V (2,…

A: Given that, Let ∠TSV=θ and ∠VSR=θ(∵SV is angle bisector)

Q: a) Check that the line r: (x, y, z) = (1,0,1) + t(1, –1,0) is parallel to the plane n:x + y +z = 0;…

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