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

Q: nd the length of the vector fo raight line joining the points 5,2). Also find the angle made

A: Given, The vector is formed by the straight line joining the points 1,3 and5,2. The length is to be…

Q: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

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Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

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Q: Write down the position vectors of any two points on the line ˜ r · (3i − 4j) + 2 = 0 and hence find…

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Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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Q: For what values of a and ß will the vector (a, 1, B) be orthogonal to (2, 0, 7) and (-1, 1, 2)? α =…

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Q: 4x-y+5z=0

A: If a line and a plane are perpendicular to each other then the direction vector of the line and the…

Q: Write down in normal form the equation of the line which is (a) parallel to the line r (5i +3j) = 2…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: Topic = vector

Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

A: Given query is to find the point and the parallel vector.

Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

A: topic - point and vector parallel to line

Q: given the vector, PQ, whose initial point is P(-2,-5) and whose terminal point is Q(3,4) the…

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Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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Q: For the points P = (- 4, 3) and Q = (5, - 1) write the vector v represented by the directed line…

A: For the points P = (- 4, 3) and Q = (5, - 1) Now we find vector V represented by the directed line…

Q: Let L be the line defined by the vector equation v = [ -1, -3 ] + t [ 1, -2 ]. Find the equation y =…

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Q: If the line through the point (3.-4,-1) and parallel to the vector i+j+k. The equation of the line…

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Q: Find the equation of the following lines in the form specified in bold. a) A vector equation of a…

A: As per our guidelines we are supposed to answer only one question i.e. question no (a). For the…

Q: If the line through the point (3,-4,-1) and parallel to the vector i+j+k. The equation of the line…

A: We can answer the question as false or true as below

Q: Find a vector perpendicular to the lines: 4₁: x = 3-4t y=-2-6t x = -1 + 2t y=4-t L₂: O O None of…

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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: c) Is the point (4,3, 3) on the line (L1) ? Why or why not ? d) Determine the vector equation of the…

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Q: ) Write down the position vectors of any two points on the line T·(3i – 4j)+ 2 = 0 and hence find…

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Q: Q:2) Find a vector that is parallel to the line whose equation is 5x-4 4-2z = 3 - 6y = 7 5

A: The given problem is to find the vector that is parallel to given parametric line equation, we have…

Q: What is a general equation for the line with vector equation x=[31]+t[4−5]

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Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

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Q: For the line that contains the points P(-1, 2, 4) and P2(3, 4, 7), find a) a direction vector. b) an…

A: The line contains the points P1-1, 2, 4  and  P23, 4, 7. a). Direction vector is, P1P2→=3--1, 4-2,…

Q: Determine the vector equation of a line that is perpendicular to the line, p = |-4, 4, 9 + t|-1, 3,…

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Q: The path of a particle is moving in the plane with position vector . What is the speed of the…

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Q: = Find the vector equation for the line passing through the points P₁ P₂ = (2,7-13). (5,-1,-5) and

A: The given points are;  P1=(5,-1,-5) and P2=(2,7,-13).

Q: Suppose a line is given parametrically by the equation L(t) = (5,-5,-3t,3t). What vector and point…

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Q: 4- Find the direction and direction from the point (1, 3) for which the values off do not change,…

A: 4)Given isfx,y=e2y arc tan3y3x at point 1,3A function  fx,y has no change in any direction that is…

Q: Find the equation of line passing through point P(1, –1, 2) , the direction of the line is parallel…

A: The line passes through the pointP→ = i-j+2kThe line parallel to the lineV→ = i-2i+kThe vector…

Q: Identify the DIRECTION VECTOR and a POINT on each of the following lines: (а) 7 = (3,4) + t(2, 1),…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Find the equation of the line that passes through the point ( 8, 8, 2) and parallel to the vector .…

A: The vector equation of the line which is passing through the point (h, k, l) and parallel to the…

Q: For the line €: (x, y, z) = (5, - 3, 2) + n(1, 2, - 2), find a) a point of the line. b) a direction…

A: Given parametric equation of line - x, y, z = 5,-3, 2+n1, 2,-2x, y, z = 5,-3, 2+1n, 2n,-2nx, y, z =…

Q: 4) Which of the following vectors is parallel to the line L: x = 1 -t, y = 2 + 3t, z = 5 + 2t? a)…

A: According to the guidelines we are answering first question. Please repost the remaining.…

Q: Find the vector equation of the line between the points (3, -1, 2) & (1, 4, -1), then graph the…

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Q: Find the vector form of the equation of the line in R2 that passes through P = (2, -1) and is…

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Q: For the line €: (x, y, z) = (2, 3, 4) + n(3, - 2, 5), find a) a point of the line. b) a direction…

A: the given line is: l:x,y,z=2,3,4+n3,-2,5 we have to find: (a) a point of the line. (b) a direction…

Q: Write down the line equation a) given a point Q and a vector v. b) given two points R and Q.

A: Since, our aim is to find the equation of a line that is :-(a) passing through a given point Q and a…

Q: Find a vector equation of the line r through D4 and perpendicular to the line s through F4 and B1.…

A: Given,D4→ = 1i ^ + 2j^ + 3k^Equation of line passing through D4→ is:x-1a= y-2b=z-3cThe above line is…

Q: Find an equation for the line through P(11,10) parallel to vector v=2i-3j

A: Given point on the line is P(11,10) The vector parallel to the line is,v=2i-3j

Q: Find the vector form of the equation of the line in R2 that passes through P= (2, - 1) and is…

A: If a line is parallel to another line, then they have same slope.

Q: Find the component form of the vector PQ, where P= (3,3) and Q = (5, - 8). The component form of PQ…

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Q: Consider the lines 3 - z x – 5 l1 : 2 and I. Find two unit vectors that are parallel to l1.

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Q: Find the vector equation of the line passing through the point (1, 2, - 4) and x-8 y+19 z-10 x-15 у…

A: To find the equation of line perpendicular to the given lines first we find vector perpendicular to…