Given the points A(-9,4, –1) and B(-39, –2,-31) find a parametric equation of the straight line through A and B in the form x= a+Av where a and v are vectors in R and A is a real parameter. Enter a and v in the boxes below using Maple notation. For example for the vector 2 enter < 1, 2, 3 >. a = V = Does the point C(31,13,42) lie on the straight line through A and B? O Yes, C lies on the straight line through A and B. O No, C does not lie on the straight line through A and B.

Q: Given the point A(2,1,-3) and B(6,-1,-5) write the vector equation and the parametric equations of…

A: Once we get vector form of the equation we can easily write the parametric form of equation of line.

Q: (-1,4, 12) + (3i – 6j – 14k)

A: We get the sum of the vectors as…

Q: A line passes through the point (9,1, – 1), and is parallel to the vector 7i + 3j + 7k. Find the…

A: We find the direction cosine first. As we know that the line is parallel to 7i+3j+7k So the…

Q: Draw the vector V that goes from the origin to the given point. Then write V in componentform (a, b)…

A: The given vector is -6,-4. Now, draw the given vector by an arrow from the origin to the given…

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: Describe the graph of the equation: r = 4ti – 8j + (1 + 2t)k. [Choose the correct answer.] The…

A: It is three dimensional, so each points must have three components (x,y,z).

Q: 2. Given a line that passes through the point (-2,1,3) and is parallel to the line joining A(1,5,3)…

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Q: 2. Let G and H be the points G (4, 5) and H(11, -8). 2a Find the vector HG in component form: HG 4…

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Q: 1. Given three points A(1,-2), B(2,-1), and C(0,3). Determine: a. Equation of the line through A and…

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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: Evaluate: if vector OA = (2,3) and OB (-1,-2) Show all steps please

A: if a vector is of the form  a→=a1,a2  then a→=a12+a22 see  below the answer

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: Describe the solutions of the first system of equations below in parametric vector form. Provide a…

A: (.)  Given system of linear equation is,               3x1+3x2+6x3=12-9x1-9x2-18x3=-36…

Q: Describe the graph of the equation: r = 4ri – 8j + (1 + 2t)k. [Choose the correct answer.]

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Q: Describe all solutions of Ax = b, where [2-5 3] A= -2 6-5 and b = -4 7 0 2 19 Describe the general…

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Q: Solve the problem. Describe all solutions of Ax = b, where 2-5 31 A= = [] = [] -2 6-5 and b 4 7 0,…

A: Given: A=2-53-26-5-470 and b=-38-9. To Do: Describe the general solution in parametric vector form.

Q: DONT USE AI 4. Consider the line I that passes through the points P(2,0,10) and Q(8,4,9). Answer…

A: Given that the  given line I  is  passes through  the points P  and .(a)  We  have  to  find the…

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: 1. Draw the vector V that goes from the origin to the point (-4, -6). (a) Find V (b) Write V in…

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Q: perpendicular to (x, y, z) = (1, -2,0) + r(1, -1, 1) through P(1, 3,5) [parametric equations]

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Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

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Q: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the vestun . il 1:= V2: V3: and u where a E R. (a) For which values of a is the span(v1,…

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Q: Consider the point P(-2,3) on the coordinate system. Describe geometrically the position vector…

A: Given point P (2,3)