1. Given that ZA, ZB, ZC, ZD e {angles} such that ZA and ZB are supplementary angles, ZC and ZD are supplementary angles, and ZA ZD. Prove that ZC ZB.

Q: 5) If w = 4i + 4j, find 2w. 6) If v = 3i - 5j and w = -7i + 4j, find 3v - 4w. 7) If v = -4i + 4j,…

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Q: Let u = (1, 2, 3), v = (4, 4, –2), and w = (6, 5, -5). Find z, where 2u + v - w + 3z = 0.

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Q: Prove AB and Let B, be a point on AC such that AB, = AC. 8. Let AABC be a triangle. Let C1 be a…

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Q: 9. Find the point C such that AC = ² AB. 4

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Q: 2. Let ABC be a triangle with AB = 3, BC = √3 and CA = √√3. Let XYZ be a triangle with XY = 3√3,…

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Q: Let a and m be real numbers, u = (1, a, 2, m, -3), and w = (2, а, 2, т, 3). Then the distance…

A: Let's find.

Q: onsider rectangle QRST with QR=ST=4QR=ST=4 centimeters and RS=QT=2RS=QT=2 centimeters. If point U is…

A: Consider rectangle QRST with QR=ST=4QR=ST=4 centimeters and RS=QT=2RS=QT=2 centimeters. If point U…

Q: 6. If a series £u, converges to the sum u then so does any series obtained from Eu, by +he torms in…

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Q: If AB=3x+1, DC = 2x+7, AD = 2x-1, BC = x+5 and x = 6, prove that ABCD is a parallelogram

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Q: Show that a triangle with vertices at A(−1, 2), B(4, 1), and C(5, 6) is isosceles. Distance from…

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Q: Q6) If the point A, B, C are .collinear then AB.BC = 0 F

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Q: 1. Let u = (1,2,3) and v= (1, x, 0) and w= (0,1,0). a. Find ||u + w||. b. Find (u, u + w) + ||u||.…

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Q: 12. If a b = √3 and a × b = (1,2,2), find the angle between a and b.

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Q: Let → a = and → b = . Find k so that → a and → b will be orthogonal (form a 90 degree angle). Let…

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Q: Suppose v = (2, 5, 4), |w| = 3 and the angle between v and w is 30◦ (a) Find v · w (b) Find compvw…

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Q: Prove that if two triangles have two sides of one respectively equal to two sides of the other and…

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Q: Find the area of parallelogram ABCD with vertice A(7,5,2), B(-1,2,9), C(6, –3, -4) and D(5,7,3).…

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Q: let u = <1, 2, 2> , v = <1, -1, -1>, w = <1, 3, -1> , and z = <2, 11, 8>.…

A: Given: u1 is parallel to u, u2 is parallel to v, and u3 is parallel to w.So, u1= au , u2=bv and…

Q: 2. Find the midpoint of Segment AB, where Point A is at (-5,1) and Point B is at (15,8). O (5, 3.5)…

A: Mid point of a line segment is a point which is equidistant from the two endpoints of the line…

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: 3- The result of dot product between A=(2, 3, 1) and B=(-1, 5, 1) is: a) A. B=14 b) A. B=-34 c)…

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Q: 8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

A: We will use direct formula to find the angle. The detailed solution is as follows below:

Q: Find the interior angles of traingle ABC Al B(1,0,1) P c(2,1y-1). A

A: Given: A(1,2,1), B(1,0,1) & C(2,1,-1)

Q: 1) Find the area of the triangle P(-2, -6, -1), Q (-2,-4, 1), R(3,6,6)

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Q: 11. Determine the angle between d = (3, –4, –1) and b = (0, 5, 2). %3D

A: The angle between two vectors is defined as cosθ=a→.b→ab Here the vectors and their components are…

Q: Prove that a. V. (A + B) = V.A + V.B b. V. (ØA) = (V. Ø). A + Ø(V. A)

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