Q1: al Find parametric and vector equations for the line y-axis, then find the distant between the line and the point (-1, -2,-3).

Q: 2. Find an equation (parametric and vector form) of the line if the line is perpendicular to the…

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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: Express the vector == 7= Z+ y. -22] 10 as a linear combination of = -(-3) and y=

A: Consider the vector v→=-2210. To express it as linear combination of vectors x→=-4-5 and y→=1-5.…

Q: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

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: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

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Q: M] - [8] x+y -3x+y.

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

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Q: Determine the angle that the vector [-1, -1] makes with the positive horizontal X-axis

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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: 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: Let / denote the line in R with equation y = = 3x - 2. Let Q = (2, -1). (a) Write the line / in…

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Q: Calculate the sum of the vectors that can be drawn as a vecto from the vertices of the triangle…

A: The vertices of the triangle is A7,4,-4, B1,-1,1 and C-8,-1,3

Q: Consider the line passing through the points (2, -3,4) and (5,10, -12). Describe the line by a.…

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Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: Consider the function f(x, y) = (e* - 2x) sin(y). Suppose S is the surface z = f(x, y). (a) Find a…

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Q: The position of a moving particle in space is vgiven by r(t) = (- 76- 21) i + (108t° - 2890) j +…

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