20. Which of the following is a direction vector for the plane with Cartesian equation 3x-2y-52+3-07 c. d =(-1,1,1) a. a = (1,-1,1) b. d =(3,-2,-5) d. d =(3,2,5) 21. Which of the following vectors is perpendicular to the line passing through the points P(2,3) and Q(7,10)? c. V=(7,-5) a. v = (-10,7) b. v =(5,7) d. v = (-3,2)

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: Point P₁ lies on the line {₁:[4,4,-3]+t[2,1,−1],tER, and point P2 lies on the line…

A: Solution : Given that the lines l1 : 4,4,-3+t2,1,-1l2 : -2,-7,2+s3,2,-3

Q: The line (x-22-3, y = 2z) intersects the plane (x+3y-2+4= 0) at the point P, Find: a) the…

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Q: III. Consider the line ₁ given by the symmetric equations +1=-y-1 B 2 and the line ₂ given by the…

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Q: Give the vector equation of the line passing through P and Q

A: To find the equation of the line passing through P and Q.

Q: 3) Find equations for the lines: The line through the point D/2 g. The line through (0,-7,0)…

A: Equation of line in 3D

Q: Which of the following equations define the plane passing through the points (3,0, 0), (0, –7,0),…

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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. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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Q: - 3)² = 81 then, find its ce or a=<3, -1

A: 1. Given: The points are 2,3,-6 and -1, 4, 5 To find the distance between the given points. The…

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: Find the equation of the plane through the points P (1,-1, 1) Q = (3,–1,3); R= (2,1,1).

A: We will find out the required equation of plane.

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: Let A = (1, –1, 2) and B = (4, –2, 3). Solve for proj,B. %3D

A: As per the guidelines for the multiple questions I had solved the first question.

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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