1. Express in terms of i,j, and K, given that V is equivalent to the directed line segment PQ, where the rectangular coordinates of P and Q are given Also find another directed line segment equivalent. to v. P(2,0,3), (1,4,-3) 2. Find a unit vector u in the direction of. Express u in terms of i,j, and k. V= 3; f2j- 4K Find the directed line segment AB equivalent to the vector v 3. from the information given * y= 2it j-3k, A (1,2,-1) * Y= 1-2j12; midpoint of the segment AB has coordinates (2,-1,4). 3 of the distance from A to B *y-it-ak; the point 4 has coordinates (1,0, 2). 4. Find a vector u in the direction of x= -itj-k and having half the length of y

Q: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D a. Write the unit vector for S b.…

A: This question can be solved using the concept of unit vector and linear combination of vectors.

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Three vectors V1, V2, and V3 are given. If they are linearly independent, show this; otherwise, find…

A: The given three vectors are v1​=⎣⎢⎡​103​⎦⎥⎤​,v2​=⎣⎢⎡​3−512​⎦⎥⎤​ and v3​=⎣⎢⎡​3−714​⎦⎥⎤​.Writing them…

Q: Let u be a vector. Select the most correct statement.A. The vector 4u could be longer or shorter…

A: The objective of the question is to understand the relationship between the vectors 4u and -5u.

Q: Given u = , v = -5i - j, and w (AB) is defined by the points (1, 6) and (-2, 8). a Find v in…

A: This is  a problem of vector. By dissolving vector in x and y parts we will convert it into…

Q: Solve the problem. Find the area of the triangle determined by the points P(-3, 6, -4), Q( 2, 10,…

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Q: =3. Let a = [2₁1,-1], 5o = [4₁-5, 3] and C-[-1,-2,5]. compute ax (b + c). Show full steps.

A: We have to solve given Questions.

Q: 2. Let vectors a = (3, 1, 2), b = (0, 2, 1), and c = (1, 1, -1) be given. Find (2a + 3b). c. • Find…

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Q: Draw position vector OP = (-2,-4,3) on the axis below.

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Q: Define the points P(0,0) and Q( - 7,2). For the vector PQ, do the following. a. Sketch the vector in…

A: See attached file for a step by step explanation.

Q: Consider each A and B vector, make each of the following below TRUE or FALSE, and give brief…

A: To prove: A+B→ < A→OrA+B→2 < A→2…

Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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Q: 13. Given the points A(3,5) and B( – 3, – 7), find a. the vector equation of the line.

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Q: Let A, B, C be three points with position vectors a, b, c respectively. You may assume that the…

A: Given that A, B, C be three points with position vectors a, b, c respectively. Assume that the…