Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B > 2, where does it lie relative to the line? • What is the relationship of vector v = [2, 1]T to this line? • What is the distance from origin to this line?

Q: be the line through the point with coordinates (0,1,0) in the direction of the vector h of the…

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Q: The unit vector of the PQ (of point P(-3, 4, 1) and terminal point Q(-5, 2, 2)). - The angle between…

A: here we have

Q: we consider the equations of a line in symmetricform, when a = 0, b = 0, c = 0.x − x0/a = y − y0/b =…

A: Given, Point P0(-2,3,3) with direction vector, v=(2,4,3)

Q: 5. (a) Given A = a,5-ay2 + a₂, find the expression of a unit vector of B such that B/A and BL A, if…

A: Solution 5(a): Given that A→=5ax-2ay+az and  B→∥A→ if B→ lies in the xy-plane. So, B→=5bx-2by. Unit…

Q: 5. In each case, find the equation of the line with the given properties. (a) Passing through the…

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Q: The line ℓ is given by the equations x −2y + z = 2 and x + y −3z = 4. That is, ℓ consists of all…

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Q: Let I be the line with parametric equations x = -9-2t y=-10+3t z=4+t Find the vector equation for a…

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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: Which of the following vectors is/not perpendicular to the line whose direction vector is (2,-3,5)?…

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Q: Describe all points Q = (a, b, c) such that the line through Q with direction vector v intersects…

A: Given: To Find: All points Q = (a, b, c) such that the line through Q with direction vector v…

Q: Consider the line that contains the point (2, -3, 5) and that has the direction vector (1, 2, 4). a)…

A: Given: The line passing through the point 2,-3,5 and having direction vector 1,2,4, To find: The…

Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

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Q: x-1 y+3 12-z Consider the following lines defined by I,: and l2: 9. =- %D 7 x = 2t + 10, y = 5t, z…

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Q: alculate (a) ?500 (2i + 5). i=0 (b) the sum of the first 50 multiples of 3 (starting from 3, not…

A: Given 500 (2i + 5).for i=0

Q: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: What three points are on the line L: vector r= (2,-5) + s(2,1), sER

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Q: What is the shortest distance d from the line L₁ defined by the vector equation to the line L₂…

A: Consider 2 lines in vector form as: v1 = a1 + c * b v2 = a2 + d * b here, c and d are the constants.…

Q: 1. A line L passes throught point (2,-1,5) that is parallel to line given by l(t) = (t, −1+t, 2).…

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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: Let /be the line through the point with coordinates (2,-1,0) in the direction of the vector G) 1…

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Q: Q6\ Find parametric equations for line through P(-3, 2, -3) and Q(1, -1, 4)

A: P(-3,2,-3) and Q(1,-1,4).