20. Consider lines €1 and l2. l1 : [x, y] = [1, 4] + [[-7, 2] l2 : [x, y] = [-2, 6] + t[k, 9] a) For what value of k are the lines parallel? b) For what value of k are the lines perpendicular?

Q: Determine whether the pair of lines listed is parallel, perpendicular or neither y = x+3 y = 4x5 y =…

A: We have to find parallel, perpendicular line from the given lines. Two lines are parallel if their…

Q: Find b such that (2, -1), (3, 2), and (b, 5) lie on a line.

A:

Q: 5- Find the Line that passes through the point (l,2) and througgh the point of inter Section of the…

A: In this question given that point (1,2). And two lines x +2y = 3 and 2x -3y = -1. And we find that…

Q: 9. The points (1, 2), (5, A), (A, 7) lie on a straight line. Find all possible values for A.

A:

Q: Find the point on the line x - 3y+9 = 0 that is closest to the point (-1, 3). 1) (-0.9, 2.7) O 2)…

A: Closest distance form a point to a line is normal distance from point to line.

Q: + 4x-21- 27. What are the x-intercepts of the graph of R5)--x- 20 A. 7, -3 B. -4, 5 C. -7, 3 D. 4,…

A:

Q: from one point to another, or [x₁ − x₂] + |y₁ - y₂ for points (x₁, y₁) & (x2, Y2). Plot A(2, 5). A)…

A:

Q: Find k so that the line through (– 3,2) and (k,4) is a) parallel to 5y- 2x = 1; b) perpendicular to…

A:

Q: r1(t) = (3, –6, 2) +t (-4, 2, –4) r2(t) = (-3, 3, – 10) + t (2, 1, 0) Find the point of…

A: Lines r1 and r2 can be rewritten as follows:

Q: determine if the two lines are parallel, orthogonal or neither. n) The line by i=(4– 7t,-10+5t,21–…

A: Given

Q: 1. Write the line parallel to y = -2x + 5 that passes through the point (1,1). a. y = -2x + 1 b. y…

A: Question 1 - The equation of line is given as - y = -2x + 5 Comparing the above line with the…

Q: Find the point where the two lines +s and +t intersect, if it exists

A: We need to find point where lines intersect.

Q: 3. Find PQ rounded to the nearest tenth. (Hint: use distance formula)

A:

Q: Q)Suppose that one line is parallel y=13x+ 13 and passes through (15,7). Where does that line cross…

A: Given :  y=13x+ 13  compare with y = mx + c slope m = 13

Q: The point of intersection of two lines 2x + 3y = 6 and x - 3y = 5 4 is (4, 9. O True O False

A: False Because the point of intersection of two lines 2x+3y=6 and x-3y=5 is (113,-49)

Q: The line that is perpendicular to the lines r = ⟨4t, 1 + 2t, 3t⟩ and R = ⟨-1 + s, -7 + 2s, -12 +…

A: The given lines r→=j^+t4i^+2j^+3k^R→=-i^-7j^-12k^+si^+2j^+3k^ Let,  4i^+2j^+3k^=b1→i^+2j^+3k^=b2→ As…

Q: Determine the midpoint of the line segment between A and B shown below: 2 -3 -2 -1 1 2 3 -1 -2 - -3…

A: It can be observed that the point A is and the point B is . According to the Midpoint formula, the…

Q: 25. (17,-7) (-8, 11) Parallel: Perpendicular:

A:

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y=x and y=2-x…

A:

Q: . Which three points are on the line L: r = (2,-5)+s(2,1), s € R? a. Q(2,1), 0(6,-3), R(2,-5) b.…

A: Explanation of the answer is as follows

Q: a.) (-3,4); parallel to y=3x-5 b.) (-2,-4); perpendicular to y 2/3x-5

A: (a).   The given equation of line: y=3x-5 Slope of line parallel to the given line is: m=3

Q: 25. Determine the x- and y-intercepts. a) [x, y] = [2, –4] + t[3, –1] b) [x, y] = [-8, 11] + t[5, 2]…

A: The given equations are in parametric form. To find x-intercept put y=0 and get the value of…

Q: 2. Which point is the intersection of x + 2y = 8 and 2x + 3y = 10? a. (-2, 5) %3D b. (-4, 6) с. (2,…

A: The given equations are x+2y=8          …12x+3y=10      …2

Q: - Classify the following lines as parallel or perpendicular or neiti a- y=4x-7 & y=4x+9. b- y=-5x+1…

A: Given: a. y=4x-7  and y=4x+9b. y=-5x+1  and y=3-5xc. y=12x and x=12y Concept Used: Two lines are…

Q: Find the value of X such that and are perpendicular

A:

Q: Which line is the same as [x, y] = [1, -8]++[4, −3]? a) [x, y]=[2, 4]++[4, -3] b) [x, y]= [1,…

A:

Q: Which of the following ordered pairs satisfy the 7x+8y0? а. (1,-5) b. (5,-1) . с. (1,1) • d. (0,0)

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.