24. Diagonal of parallelogram Show that the indicated diagonal of the parallelogram determined by vectors u and v bisects the angle between u and v if |u| = |v|. %3D

Q: Find the area of the triangle with the given vertices. (Hint: 1lu x v|| is the area of the triangle…

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Q: Use vectors to find the lengths of the diagonals of the parallelograr that has i +j and i – 18j as…

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Q: The area of the parallelogram formed by the vectors p = (a, 1, –1), and q= (1,1, 2) is v35 sq units.…

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Q: Use vectors to find the interior angles of the triangle with the given vertices. (Round your answers…

A: We have to find the angles of the traingle.

Q: Suppose u = (-3, 2) and v = (10, 2) are two vectors that form the sides of a parallelogram. Then the…

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Q: Find the angle between u = (2,3,1), and v = (-3,2,0)

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Q: se vectors to determine whether the triangle with vertices A = (1,–3,–2), = (6,–2, -5) is…

A: we know that if the dot product of two vectors is zero then the two vectors are perpendicular.…

Q: A triangle in R3 has two sides represented by the vectors = (1, 3, –2) and = (2, 7, 3). Determine…

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i+j and i – 2j as…

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Q: Consider the triangle with vertices P(-1, -4, -3), Q(0, –1, –5), and R(4, –3, –-6). Determine the…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Solution: we know that u→=ucosθ i +usinθ j

Q: 1. Solve for the interior angles (in degree) of H and I of the triangle defined by the three points…

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Q: Consider the triangle with vertices P(3, -4, 0), Q(4, -1, -2), and R(8, -3, -3). Determine the…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: This is a question of vector algebra. Kindly see the uploaded answer for detailed solution

Q: Verify a Right Triangle:(a) find the length of each side of the right triangle, and (b) show that…

A: We know that, the distance d between two points x1,y1 and x2,y2 is given as d=x2-x12+y2-y12…

Q: (b) Find the area of a triangle with the points A(1,0, 0), B(0,1,0), C(0,0, 1) as it vertices by…

A: (b) We have to find area of triangle with the points A1,0,0 , B0,1,0 and C0,0,1 by using cross…

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Here, given that u=9, v=2, θu=0°, θv=60°

Q: Determine the value(s) of k such that the area of the parallelogram formed by the vectors a = (k +…

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Q: Use vectors to find the interior angles of the triangle with the given vertices. (Round your answers…

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Q: 5. In the parallelogram RSTU, the diagonals RT and SU intersect at point W. T. If RW: 2x +2 and RT =…

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Q: 1. Find the distance between p(-2, 3,0) and Q(2,1,5). 2. Find the direction of A = 2i - 3j+7k. 3.…

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Q: ±). 1.4 Use vectors to decide whether the triangle with vertices P(1,–3,–2), Q(2,0, –4) and R(6, –2,…

A: solution of the given problem is below ...

Q: 2. The angle e between the vectors u and v satisfies cos 0 = So if u and v are perpendicular, then…

A: The angle between two vectors is, cosθ=u·vu v The vectors are perpendicular if u·v=0. The given…

Q: B) Use vectors to check whether the points A (1,-1,0), B (2,1,-1), and C (-1,1,2), are vertices of a…

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Q: Given the attached picture determine whether the cross product of vectors w and v is directed into…

A: We must know that cross product of any two vectors will result in a vector that has the direction…

Q: Given perpendicular vectors a = (5,3,-1) and 6=(2,2,k), find ||||.

A: Given perpendicular vectors a→=5, 3, -1,     b→=2, 2, k   To Find: b→

Q: The inequality a ob < 0 imples that the angle between the two vectors is O obtuse O the right angle…

A: From given information

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: 2. Suppose that A and B are two points on opposite ends of the diameter of a circle. Let C be any…

A: Explained below

Q: 1. A(1,2,-3), B(3,4,-2), C(3,-2,1) is an isosceles triangle. II. P(-2,4,0), Q(1,2,-1), R(-1,1,2) is…

A: I. Distance between AB, BC, AC are calculated for isosceles triangle AB=3-12+4-22+-2-32 =4+4+25=33…

Q: 18. The sides of a rectangle are formed by vectors A and B with |A =2 and B = 5. Determine the area…

A: Explanation and solutions is given below...

Q: A triangle in R3 has two sides represented by the vectors = (2, 3, –1) and OR = (1, 4, 1). Determine…

A: Topic:- vector algebra

Q: (b) Consider the vectors u = (3,0) and 7 = (5,5). (i.) Find the size of the acute angle between u…

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Q: b) Determine the gradient of each side of the triangle c) Using your answers in a) and b), justify…

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Q: The distance d of a point P to the line through points 4 and B is the length of the component of P…

A: If a vector passes through the points Cx1, y1 and Dx2, y2, then its position vector is defined as…

Q: 3. (a) Define the dot product of the vectors u = (a,, az) and v = (b,, b,), and state the formula…

A: a). The dot product of the vectors u=a1, a2  &amp;  v=b1, b2 is the sum of the product of…

Q: 17R(1,1,3), S(3,-3,6) and U(-2,4,7) are three vertices of parallelogram RSTU. a) Find the…

A: Given that the three vertices of a parallelogram RSTU are R1,1,3, S3,-3,6 and U-2,4,7 Now, let the…

Q: Use vectors to find the interior angles of the triangle with the given vertices. (Round your answers…

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Q: 7. Given the vectors v1 = (1, –1, 1), v2 = (1, 1,0) and v3 = (2,0, 0). Find lengths of the vectors.…

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Q: If a = (2, –1, 2) and b = (3, 2, 1), answer the following. Vectors can be entered using either or…

A: Given a=2,-1,2 and b=3,2,1

Q: Use vectors to find the interior angles of the triangle with the given vertices. (Round your answers…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: This question is based on vectors.

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: 3)Using vectors to find the area of triangle ABC,ifA(1,1),B(0,0) and C(-2,-1).

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Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A: Distance from line in 3D

Q: If u = (1,3, –2) and v = (2,–1,4). Find the distance between the vectors d(u, v) and d(v,u). %3D

A: Consider the given vectors u=1 , 3 ,-2  ,  v=2 , -1 ,4 First, find the difference of the vectors u…

Q: The vectors (8, k) and (9, 6) are perpendicular. Find the value of k.

A: The vectors (8, k) and (9, 6) are perpendicular

Q: (i) Find the direction cosines for v = 2, 3, 4 .  (ii) Verify that the sum of their squares equals…

A: We know that If the vector is xi+yj+zk=(x,y,z) and  r=length of x,y,z =√(x2+y2+z2) Then the…