Let C₁ denote the positively oriented boundary c and let C₂ be the pa the lines x = ±1 and y=±1 shown below. Explain why 1 C₁ C₂ 4 X S. - dz 2z² +1

Q: Let L : +t 2 be a line and P(5, –1, -2) a point. Let Q be the closest point on L to P. !! a) Find…

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Q: Specify m to distance from point M (1;0) to the lines (Δ):4x+3y+m= 0 by 2.

A: Please see the below picture for detailed solution.

Q: Find the line L, that passes through the point P(1,2) and parallel to the line L2: x+2y=3.

A: Given data is: The equation of the line L2: x+2y=3 To find the equation of the line L1 that passes…

Q: 18. Find the points of intersection of the lines 4₁: R= 2i + 3j + 3k + t(i-2j + 5k) y +1 2 12: x + 3…

A: These two line not intersect

Q: (1) What is the relationship between the lines L1 and L2? where ) L1:x = 1-t, y = 4 +t, z = 2+3t…

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Q: 20b. Find the coordinates of A' after A(-3, 4) has been reflected: Reflection in the x-axis: A'= I…

A: To find the reflections

Q: only part b

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

A: Explanation of the answer is as follows

Q: 5. Evaluate - xy+3z)ds where C is the line starting at (1,1,1) and ending at (-1,-2,-3).

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Q: Find the acute angles between the lines y = √3x - 1, y = -√3x + 2 Find the length and direction…

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Q: 4. Name the coordinates of the image of Q(-2, 5) under a translation along (x, y) → (x + 5, у - 3).

A: We have to find the name the coordinates of the image of Q(-2,5) under a translation along…

Q: Let S(x, y) = x² +y² – 2x – 16y + 10 = 0 be a circle and L(x,y) = x – 5y + 10 = 0 be a line. 1. Find…

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Q: Q21: show that the line x=-1+t,y:3+2t, 2=-t dud the plone 2x-24-z=-3 are paralle . Find the diitance…

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Q: What is the relationship between the lines L1 and L2? where L:x = 1- 2t, y = 3+ 3t, z = 5+3t L2:x =…

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Q: y+1 O Determine the angle between the lines 7 – x = and 2æ – 9y + 7 = 0 [k2] -

A: Given that  The two lines are  To find the angle between the two lines

Q: Determine if the following two lines are parallel, coincident or distinct: h:ri= (-5,-3, 1] + t (-3,…

A: The given lines are                          l1 : r1→=-5, -3, 1+t-3, 1, 0 ; t∈ℝ…

Q: 2. Which of the following lines in standard form is equivalent to y OA. 2x+y=1 OB. x + 2y = 1 Oc.…

A: We have given that y = 2x + 1

Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: 4. Find the values of x and y as shown below if three lines are parallel. (5y-4) 3y (2x+13)

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Q: What is the relationship between the lines L1 and L2? where L1:x = 1-t, y = 1+ 2t, z = 2-t L2:x =…

A: The given lines are:L1: x=1-t ; y=1+2t ; z=2-tL2: x=1+t ; y=1-t ; z=2-3t

Q: -5 Let L : +t 4 be a line and P(-1,–2, 1) a point. Let Q be the closest point on L to P. %3D 4 a)…

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Q: Find the angle between the following pair of lines: £ =2? =5] +k + 2(3 + 23 + 6k) and = 7i — 6k +…

A: A vector in the three dimensional space is represented by v=ai∧+bj∧+ck∧, where a, b and c are the…

Q: Q2 P. y=f(x)

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Q: 3. Plot each of the points below and give their coordinates in the specified coordinate system. a.…

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