Use vectors to find the lengths of the diagonals of the parallelogram that has i+j and i – 2j as adjacent sides Show that (4, 5, 2). (1, 7, 3), and (2, 4, 5) are vertices of an equilateral triangle.

Q: Use vectors to decide whether the triangle with vertices P(3, -1, -4), Q(4, 2, -6), and R(8, 0, -7)…

A: NOTE: Refresh your page if you can't see any equations. . given vertices are

Q: The dot product of vectors p = (3, -5) and q = (15,9) is A/

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Q: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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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 the vectors u = (1,-3,5) and v=(2,1,-3) to Find 1 the area of the parallelogram determined by u…

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Q: If u = 5i - j+ k, v =j - 5k, w = -15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)…

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Q: A parallelogram is determined by the vectors = (-2, 5) and 7= (3, 2). Determine the angle between…

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Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: Consider vectors, 2 u = |2, v = w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find…

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Q: Find the unit vector orthogonal to the plane through the points P ( 12, 3, -4 ), Q (-1, -2, 2), and…

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Q: Find vector V such that the vector has a length of 16 and makes an angle of n/3 with the x-axis.

A: Given problem:- Find vector V such that the vector has a length of 16 and makes an angle of π/3 with…

Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

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Q: Use vectors to show that the points form the vertices of a parallelogram. (2, 9, 1), (3, 11, 4), (0,…

A: Given: A=(2,9,1) ,B=(3,11,4),C=(0,10,2),(1,12,5) To Show: Given points form the vertices of a…

Q: Two vectors (M = 4ax-bay) and (N = 6ax-2ay-Saz), find the vector perpendicular to these vectors?

A: Given Vectors are                                                 M=4ax-6ayN=6ax-2ay-5az vector…

Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: Find the resultant of the vectors A and B. Ả = A = 8a, + 7ay + 2a, B = -Зах — 8ау — ба, Draw the…

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Q: Prove that the points with position vectors a+2b, 2a−b and 3a−4b are collinear.

A: We have to use determinant method to solve.

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

A: Given  AB=i+4j-2k and B is the point (5,1,3)

Q: Consider the vectors ā = 2i+3- k, č = i+ j+3k d = 21-j+ k, j = -21- j+ k. Which pairs (if any) of…

A: As per Bartleby's answering policy, we can answer only one question with a maximum of three subparts…

Q: For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

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Q: Find all values of b for which the vectors (2, -4, 5) and (b2, b, 0) are orthogonal. (Enter your…

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Q: For the vectors u= (-8,0,3) and v= (1,3,-3), calculate proj,u and scalvu.

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Q: Suppose u = (0, –2) and v = (2, 2) are two vectors that form the sides of a parallelogram. Then the…

A: This question is based on parallelogram diagonal.

Q: Calculate the values of a and b so that points A (1,1,1), B( a,2,b) and C(1.0,0) are aligned…

A: If two vector are collinear , then they are scalar multiple of each other. that is AB→=λAC let a ,…

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are he vertices of a…

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Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

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Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(-1, 1, 5) P2(2, 5,…

A: Given Points - P1 = -1, 1, 5P2 = 2, 5, 0Vector P1 and P2 ,P1→ = -i+j+5k…

Q: The vectors v = (3, 4) is projected onto the x-axis The length of the projection is %3D A/

A: We have to find

Q: (a) For the vectors d = (2, p, 8) and b = (q, 4, 12), determine values of p and q so that the…

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Q: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: Find two vectors v1 and v2 whose sum is , where v1 is parallel to while v2 is perpendicular to . v1…

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Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(1, 4, 5) P2(4, -2,…

A: Given that P1 1, 4, 5   and  P2 4, -2, 7. Compute the direction of vector P1P2 as follows.…

Q: Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,–4) and R(6,–2,-5) is…

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Q: If two vectors p and q are such that |p| = |q, show that p + q and p- q are (This proves that the…

A: Given p=qwe know that two vectors are perpendicular iff their dot product is zero

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: 10,7 and -2,-75

Q: Find the measures of the angles of the triangle whose vertices are A = * .(-1, 0), B = (2, 1), and C…

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Q: Consider the vectors u = (7,1,5, -5) and i = (3,4, c, 0) in R*. a. Find the value of c that will…

A: Given, The unit vector is in the same direction as u→=7,1,5,-5.

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

A: The diagonals of the parallelogram are u+v and u-v then we find the lengths of diagonal.

Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

Q: Check whether u = 6i – 2j+k and v= -4i – 3j+9k are parallel or not. Then, find the area of triangle…

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Q: Use vectors to show that the triangle with vertices (-2, 2), (4, 10), and (20, –2) is a right…

A: vector method to find right angle triangle.

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: a) If u and v are two-dimensional vectors, we calculate the dot product as   u=(u, u2) and v=(v1,…

Q: b. Find the angle between the vectors u = (18, –1, –7) and v = (-37,35, 2)

A: u = (18, -1, -7),  ∥ u ∥ = √[(18)2+(-1)2+(-7)2] = √374 v = (-37, 35, 2), ∥ v ∥ =…

Q: Calculate the area of ​​the parallelogram spanned by the vectors and .the⃗ ( 3 ; - 3 ; 1 )a→(3;−3;1)…

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Q: Find the area of the parallelogram that has the vectors u (2,-1, 3) and v (4, -5, 1) as adjacent…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: Find the acute angle between the two vectors A = 2a, +a, + 3a, and B = ax – 3ay + 2a, by using the…

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Q: 10. Calculate the area of the parallelogram formed by the vectors a =(3, 2,-2) and b = (2,-1,2).

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Q: 2. Given vectors x = (6,2) and y = (4, –3), graph the resultant of x-y using either the head-to-tail…

A: Here vectors are given as, x = (6,2) and y = (4,-3). Now  x - y = (6,2) - (4,-3) =(6-4, 2-(-3))…