(It may help to draw a picture for this question). Let A, B, C be three points with position vectors a, b, c respectively. You may assume that the three points A, B, C do not all lie on the same straight line. Let D, E, F be the midpoints of the line-segments BC, AC, AB respectively. The point with position vector (a+b+c) The point with position vector/1 a+b The point with position vector a+b+c Choose... Choose... Choose... ◆

Q: Let P(-2,–2,0), P,(1,0,–2), and P,(0, –4,–3) are three points of a triangle, Compute the vectors of…

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Q: What do coordinates mean?

A: Coordinates are set of points that defines exact position of a point in XY-plane.

Q: the diagram above, draw and label each of the following vectors. You must aper being as precise as…

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Q: iven the vectors a = (3,2,-1) and b = (1, -2,3), find the equation of the line joining a nd b. Show…

A: This is a problem of 3D geometry and calculus.

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: Which of the follow is the direction vector of the line 7=(2, 1, 3) + t(-7, 1, 6) (7, 1, 6) O(-7, 1,…

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Q: Three vectors are given: A =il+j2+23,B= &4-§2+23, and C= -x4. Calculate: (a) A+B+C. (b) A+B-2C. (c)…

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Q: 1 Determine a vector equation of the line passing through the points A(-2, 0, 0), and B(0, 1, –3). *…

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Q: Define the points P = (-4, 6) and Q = (2, 4). Find the position vector corresponding to På. %3D %3D…

A: We will find the position vector of PQ as following

Q: If a point A, the position vector ai + bj lies on the line L, vector equations r = 2i +5j +c(i-i),…

A: To find the value of (a), we need to ensure that the position vector of point A, (ai + bj), lies on…

Q: s of a and b for which the following vectors a + b, 24), v = (-10, 15, a - b) D, b = 2 9, b = 2

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Q: Given vector (-2,6) and a point (3,2) a. Write a vector equation  b. Write the vector equation as…

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Q: 2. Below are 4 vectors in component form. Graph these vectors in standard position and then find…

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Q: The position vectors of the points A, B, C, D are given by a = 2i + 3j - k, b = 4j+ 5k, c = 7i-3k,…

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Q: Either a triangle whose vertices are A(-2, -1, 3), B(7, 8, -4) and C(5, 0, 2). Using an operation on…

A: Given: Vertices of a triangle: A-2, -1, 3, B7, 8, -4,C5, 0, 2We need to determine whether the…

Q: A point A(-5,-3) is translated by the vector v = , and then reflected about the line y=0. the…

A: Given that: A(-5, -3) is translated by v=<8, 0>

Q: Plot the points in same three-dimensional coordinate system and determine whether u and v are…

A: The graph is shown below:

Q: Find the vector equation of the line that goes through the point (18, 11, 20) and is perpendicular…

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Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…

Q: Given vectors a = (-3,1,2), b = (4,0,-8), c = (6,-1,4) find a vector d that satisfies 4a - 2b + 2d =…

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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: Explain how to find a vector in the direction of the line segment from Po (*o.Yo-z0) to P:…

A: We will find the vector in the direction of the given line segment.Below find the solution in the…

Q: Let u = PQ and v = PR. (a) Write u and v in component form. (4₁, 4₂) = u V P = (-2,-1), Q = (5, -1),…

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Q: Given the points A(-3,2), B(7,17), C(3,5), D(5,5), E (√5,√5), and F (4√5,- 4√√5), find the position…

A: Some points are given and we need to find out the position vectors.

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…

Q: A line passes through points A(-1,-5, 9) and B(8, 5, - 15). A vector equation for the line is 7=(-1,…

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